Make whatever choices you feel like during the conversations in the opening. When you gain control of Latha, left-clicking interacts with objects. Right- clicking examines them. You can access your inventory by moving the mouse pointer over the bottom-right corner of the screen, where the gray square is.

Pick up the blue cup on the floor. (ITEM OBTAINED: Cup)
Interact with the Comm Terminal to call the officer.
Select the following conversation choices:

"Let me out of here!"
"What is there to do here?"
"I'm so hungry..." (ITEM OBTAINED: Food Machine Token)
"That's enough."

Use a token on the food machine next to the door. (ITEMS OBTAINED: "Food", Utensil)
Use the "Food" on the camera in the upper right corner of the room.
You'll enter a mini-game involving timing: When the moving blue arrow is under the camera, left click.

The camera is now covered in food. You have an infinite amount of food, so don't worry if you miss the first couple tries.

Use the cup on the water dispenser on the right side of the room. (ITEM OBTAINED: Cup of Water)
Attempt to use the "Connect to Trance" option in your inventory window. (ITEM OBTAINED: Wetware.HLP)
Examine Wetware.HLP in your inventory. These are instructions on making your wetware nodes.
Interact with the table located to the left of the door.
Use the Utensil on the Broken Light. You'll see you need to insulate the utensil.
Use the Utensil on the Guy sleeping in the right-hand side of the room, covered in green sheets.

(ITEM OBTAINED: Piece of Plastic)

Use the Utensil on your Piece of Plastic. (ITEM OBTAINED: Rubber-covered Utensil)
Interact with the table again.
Use your Rubber-covered Utensil on the Broken Light. There should be enough space for that paper now.
Use your Documents on the Broken Light. (ITEM OBTAINED: Burning Paper)

Use your Documents on the Wastepaper Bin in the corner of the room to the right of the door.
Use your Wetware Residue on the Cup of Water.
Use the "Food" on the Cup of Water.
Use your Burning Paper on the Wastepaper Bin.
Use your Cup of Water on the Wastepaper Bin. (ITEM OBTAINED: Wetware Module)
Use the "Connect to Trance" option in your inventory on the Terminal at the left side of the room.

You'll enter a mini-game sequence. It's just like the classic "Simon Says" game.

There are four shapes which pulsate in a random order.

When they stop, you have to click on each shape in the order that they pulsated.

The first round has you doing four in a row, the second has you doing five in a row, the last has you doing six in a row.

If you're having trouble keeping up, one way you can "cheat" is with using a text editing program, like Notepad, Notepad+, or GEdit (assuming you're playing the game in windowed mode instead of full screen). Choose a letter to be associated with each of the shapes, and write a legend in your text editor. For example:

A = Upper-left shape
S = Upper-right shape
D = Bottom-left shape
F = Bottom-right shape
(you can use whichever letters you'd like, they don't have to be ASDF)

Whenever a shape flashes, type that shape's associated letter in your text editor. Then,
when they stop flashing, simply use the sequence you generated to enter the code.
For example, if you ended up with the following sequence:

AASD

you would click the upper-left shape, the upper-left shape, the upper-right shape, and the bottom-left shape, in that order.
I was going to offer a download link to a save file just after this point if you absolutely couldn't get  past it, but I don't see any of my save games in my Technobabylon 3 directory...I'm kinda curious how Technocrat managed to hide save data now. Anyway... Remember, practice makes perfect. Good luck!

After the cutscene, use your Connect to Trance option on the Guy in the bed. You'll enter another minigame sequence. There is a 5x5 grid of lights that are either red or blue. Clicking on a light toggles that light's color, as well as the colors of the lights just above, below, to the left, and to the right of it. For example, if you click on a red light surrounded by blue lights:

B
BRB
B

they'll shift into:

R
RBR
R

The goal is to bring the amount of red nodes down to an amount much smaller than is currently there. (As of this writing, I'm not sure what the exact "win" condition is; just that making the amount of red nodes as small as possible will most certainly trigger it.) After succeeding, you'll see a cutscene. (ITEM OBTAINED: Epinephrine)

The epinephrine item is not physical; like Wetware.HLP, it's data stored in Latha's brain. You need to use this data to synthesize some epinephrine in real life. Moving on:

Interact with the Comm. Terminal next to the door.
When the drone enters the room, interact with it. (ITEMS OBTAINED: Injector, Scalpel)
This is where the game can be a bit of an annoying pixel hunt; look carefully at the bottom of the table. You'll notice you can interact with the Bolts that keep it in place on the floor.

Use your Food Machine Token on the Bolts.
Look closely at the edges of the table; you'll see you can interact with the Table Edge on the left of the table.

Now that you've unscrewed the bolts...

Interact with the Table Edge.
Interact with the Table Edge again.
Having pushed it twice, it should be under the Camera.
Interact with the table.
Use your Rubber-covered Utensil on the Camera. (ITEM OBTAINED: Lens)

Use your Scalpel on the Food Machine. (ITEMS OBTAINED: Memory Module, Optical Module, Power Module)
Each of these three modules need to be repaired/modified before being replaced in the Food Machine.
Use your Epinephrine on your Memory Module.
Use your Lens on your Optical Module.
Interact with the Table Edge on the right-hand side of the table.
Interact with it again.
The table should now be below the Broken Light.
Interact with the table.
Use your Power Module on the broken light.

Now that each of the modules have been repaired/modified, proceed to replace each in the Food Machine:
Use your Memory Module on the Food Machine.
Use your Optical Module on the Food Machine.
Use your Power Module on the Food Machine.
Use your Food Machine Token on the Food Machine.
Use the Injector on Guy.
Use your "Connect to Trance" option on Guy. Watch the cutscene. (ITEM OBTAINED: Program)

Interact with the Terminal. There is a new option on the terminal, DRONE/UTL.

Select this option. You will find yourself once again in a minigame.

The goal of this one is to, judging from the position of your drone on a given map, input a set of commands that will let it walk to the terminal in front of the green square, download the security door information, and walk to the security door in front of the red square. There are four input commands: Left turn (the button labeled with the counter-clockwise rotating arrow), Right Turn (the button labeled with the clockwise rotating arrow), Move Forward (the button with an arrow pointing up), and DOWNLOAD (Labeled with the word "DOWNLOAD"). If you can't work it out, I offer here sets of instructions that will let you complete each of the three levels. If you see an instruction with a number next to it (for example, "-Move Forward (x4)"), that means do that action 4 times.

1ST LEVEL SOLUITON:

• Left Turn

• Move Forward

• Right Turn

• Move Forward (x4)

• Right Turn

• Move Forward (x2)

• Left Turn

• Move Forward

• DOWNLOAD

• Right Turn

• Right Turn

• Move Forward

• Left Turn

• Move Forward (x4)

• Right Turn

• Move Forward (x4)

• EXECUTE

2ND LEVEL SOLUTION:

• Right Turn

• Move Forward (x2)

• Right Turn

• Move Forward (x3)

• Left Turn

• Move Forward (x2)

• Right Turn

• Move Forward

• Left Turn

• Move Forward (x2)

• Left Turn

• Move Forward (x3)

• Right Turn

• Move Forward

• Left Turn

• DOWNLOAD

• Left Turn

• Move Forward

• Left Turn

• Move Forward (x3)

• Right Turn

• Move Forward (x2)

• Right Turn

• Move Forward (x5)

• Right Turn

• Move Forward

• Left Turn

• Move Forward

• Right Turn

• Move Forward (x2)

• Left Turn

• EXECUTE

3RD LEVEL SOLUTION:

• Move Forward

• Left Turn

• Move Forward (x6)

• Turn Left

• Move Forward (x2)

• Turn Left

• Move Forward (x2)

• Turn Right

• Move Forward (x3)

• Turn Right

• Move Forward (x3)

• Turn Left

• Move Forward

• DOWNLOAD

• Turn Left

• Turn Left

• Move Forward

• Turn Right

• Move Forward (x3)

• Turn Right

• Move Forward

• EXECUTE

It may take a few tries because it's easy to overlook a step.

Like with the first mini-game, with practice, you should be able to overcome this challenge.

Interact with the drone. You will see it won't let you access its storage bay.
Use "Connect to Trance" on Guy. During the cutscene, he states he'll loosen his grip on his sheets.
After the cutscene ends, interact with Guy. (ITEM OBTAINED: Large Plastic Sheet)

Use your Large Plastic Sheet on the Drone.
Interact with the Drone. (ITEM OBTAINED: Cutter)
Interact with the Table. It should currently be below the Vent just to the left of the Broken Light.
Use your Cutter on the Vent. (this will trigger the ending cutscene).

Before doing this, you could also use Connect to Trance on either the Terminal and Guy for some parting dialogue with the folks helping you escape, if you'd like.)

Watch the ending cutscene.

END GAME