I have some LEDs lighting the inside of my computer, currently powered off a AA. Is there a way to use the power wires from the PSU to power it? All the normal power wires (that go to hard drives and optical drives) are used up, if that info is needed.
Running off just one AA battery? Most LEDs would need 3.2 to 3.7 volts, not 1.5 volts. Im going to assume that your LEDs are 3.2-3.7v, 20mAh?

Although you COULD pull your power from tapping into one of the 12v lines supplying, say, your DVD drive, if you only have a few LEDs total, just tap into the power feeding one of the case-mounted USB ports. Its a nice 5v, 500mAh (or 850mAh for USB 3.0). Of course, your going to need the proper resistor to bring down the voltage down to an appropriate level.

Some pics, and/or more detailed descriptions would help a little.
Most LEDs need about 2.1V, actually, and your computer supplies 5V power. You should put one to two LEDs in series, and you MUST include a current-limiting resistor. You can then put sets of those into parallel. I definitely do not recommend tapping USB for power, as the USB spec dictates a maximum of 100mA on any USB port without explicit negotiation for more power.
Sorry about that. I was thinking the max load on USB, not the single unit load. But yes, your right about USB.

My reference to LEDs was based on what I use the most for projects and hobbies.

http://lighthouseleds.com/0402-smd-led-blue-ultra-bright-130-mcd.html
Blue LEDs tend to have the highest forward voltages. Glancing at a Cree RGB model I've been working with, red is nominal 2V, while green and blue are 3.2V nominal.

You can pretty easily (and cheaply) get a splitter to break out the +5V and +12V rails for whatever purpose you might want.
Actually, it does just use a normal 1.5 v battery. It is a nice case light, but it is really a headlamp!

All I want to do is imitate the battery, but with a PSU cable. Also, what would I do with the four wires; which are positive and which are negative?
Yellow = 12V, red = 5V. Black next to yellow is the 12V ground, and Black next to red is the 5V ground. Were there any resistors on that board, or was it connected directly to the battery? Were all three of those LEDs in parallel or series?
Lets see. There are six assorted components, and yes, a resistor. It is green with silver, bronze, red and gray stripes in that order. And I think they were in parallel; here is an interesting x-ray sort of picture:

Also, would the current of the LEDs be equal to the current of the battery? Meaning, in this case, not the LEDs themselves, since I'm actually powering a small board.
No, we could work out the current from the components. Also, I bet some of those components form a voltage booster circuit. Do you have surface photographs of both sides of the board?
Sure, here is the pic:

Don't know how you can see what the components are, precisely, though.
Yeah, something tells me - we won't learn the current from this picture. Anyone got a guess?
(bump)I think I'll just connet the wires and see if it explodes; it might work okay.
From investigating that board and trying to draw out the schematic based on the traces and components, I come up with a complete ballpark of about 20mA per LED. Try using the resistors that will generate that current and see what happens.
  
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