Is my RAM bad?

Chances are MUCH more likely its the PSU. Define not working?
Does it not come on at all?
Can you get into BIOS?

Create a memtest boot disk and try booting your PC from it if you can.
http://www.memtest86.com/download.html#R40a

If not, leave in only one stick and try then. Then try another.

Does your PSU fan turn on at all?
Do you get a beep code?
Usually with RAM issues the PC starts powering up and then either beep codes or dies after a few secs.

Two possible causes: Overheating or the Power Supply is dying... according to your information it sounds to me more likely to be overheating. Computers can overheat quickly after turning them on if the processor is not getting cooled down. If the processor fan is not running it would take the processor just a few seconds to shutdown for it's own protection.

Gaming makes the processor run harder and hotter... and if it's not getting properly cooled down, it would cause the processor to throttle down, freeze, get blue/blank screens, while the processor fan speeds up.

Adding more RAM is always good... but wait till you solve the present problem first. What you need to do, is check that the processor fan is clear of dust and lint, clean it if necessary and see if the computer then runs... try the computer on a flat surface so the fan can get in all the air it needs. If it still doesn't run, check if the power adapter is supplying enough voltage.. See how to in the video.

http://www.youtube.com/watch?v=LnTxs0o5CJA

If the power adapter is ok, and the processor fan runs normally after being cleaned and still the problem isn't solved, the processor may have suffered damage, so have the computer checked by a technician.

Your symptoms suggest two main possibilities:
1. bad fan
2. other unfixable hardware issue

Of course, run MEMTEST but I doubt that's the issue.

*Your issue sounds serious and likely unfixable by you. I hope I'm wrong.

To answer most of your questions, I can't get into the laptop at all.

The processor light blinks 3 times when the laptop turns on, and the fan goes, but nothing happens on the screen.

I've cleaned out the fan before and it worked for another week.

I've done it again but it didn't work that time.

It takes me an hour to do so, but if you guys can pinpoint the exact problem, I'd be glad to do it again.

If it worked after you cleaned the processor fan it was probably overheating... depends on what you removed from the fan, so..
Was it dust, dirt, lint balls - fuzz balls, little or more? and did you remove the same amount this time?... If you clean the fan from the ouside, it's possible it still is plugged and can only be thoroughly cleaned after opening the casing. So completely cleaning it is the only way it's going to work.... if that's not done, and you persist is making it run as it is, it's possible the processor may suffer permanent damage. So if you can't open it, have it serviced by a computer technician.

I didn't really clean much, just used a can of compressed air and blew on the fan, while still in its black casing.

The rotor of the fan itself, I couldn't open because I didn't want to mess with the electrical tape, and the whole casing wouldn't come out even after I unscrewed it.

I'll probably only have time to open it up again on Sunday, so if you can tell me specifically what to do, it'd be appreciated and helpful.

You must have missed some screws.. Watch the video on how to repair the Processor Fan. Better explained... impossible.

Toshiba » Satellite » L655D-S5093
Fan Repair Video
http://www.laptopinventory.com/LaptopInventory.php/Tosh...

That video link you provided is actually the one I was using before.

However, in that video, that laptop model differs, so it wasn't helpful when I got to the fan itself and some parts of the motherboard.