Hi, my computer has been running 24h/24h for a long time now (like 3 years) and yesterday when I got my new computer, I shut it down for a while. When came the time to boot it back up to get some files, it wouldn't. Now its hard to describe a noise.. but I could hear something in the psu like some low electric noise, a bit like if you play with 2 electric wire.. Needless to say, my computer doesnt boot and the fans barely do half a turn. Is there a way to be sure its my PSU ? Can I do some kind of PSU test ?
 
My PSU is an Antec Phantom 500 btw.
 
Thanks...

I don’t know how well you familiar with computers, but if you confident that you can follow few steps give it a try.
1. Disconnect the power cable and rest of the cables from your pc, just in case.
2. Press and hold power button for few seconds.
3. Open the side door of your case.
4. If you can, disconnect your psu from all non must devises (hard drives, optical drives, floppy etc.)
5. Disconnect all you can from your main board (data cables, usb etc. )
6. If your vga card is not onboard, live it. Just make sure it sits properly in the slot.
7. Make sure that ram modules in place. (disconnect and connect them just in case).
8. Now, when all non must hardware for the main board power up disconnected , double check everything and try to power on.
9. If the pc will turn on and you will see your main board logo, turn off the pc and connect  your hardware one at a time.
10. If not, try 2 switch vga card if you have spare, take one of the ram modules out etc.
11. Still no go, try to power on your pc with different psu.
12. Hope you won’t get to the next stage
13. But if you do, in order to recover your data you can try to connect you old hard drive to your new computer.
gl

Ok thanks Arkadi. I had already tried without any HD, but I will give it a try without pretty much everything else. It just sound weird that my PC could run without any problem with a PSU that doesnt seem to work anymore.

The PSU may just not be able to provide enough juice for the initial load of spinning up drives and fans.  Whether from capacitor aging, blown caps (PSU and/or mobo) is hard to say.

I suppose that powering up my 7800gtx is too much for it now

Sorry for double-post.

Is it possible to damage my motherboard by trying to boot with a defective PSU ? Like, you can damage it by giving it too much power, but is also true for underpowering it somehow ?

It's absolutely possible to damage your motherboard with a defective psu.  But it depends on how defective and what's wrong.  If your fans are not spinning the right way, that's almost a dead give away that it's your psu.  Unless it's the fan?  But it's doubtfully the fan since your computer won't start either.  So it's the psu.  Fans are simple and should start easily.  One exception is if your fan is plugged into your motherboard.   But here is an easy way to solve this.  Assuming that you would buy a new psu if it were shot, go to Best Buy or similar and buy one.  Install it, hook up the wires etc.  If your computer comes on, it was your psu and you needed one.  Keep it.  If not, then just return it with your receipt.    That's how I'd do it.  Good luck.