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[acemilo]

The obvious advice is to try another psu.  If it still does that with the new psu, then most likely something is wrong on the motherboard.  It may be overheating, or there may be a short or cut trace somewhere.  Try following the traces from where it plugs into the mobo to where they end, and see if there are any cuts.

[AmO]

).
Remove the HD and DVD-Rom leaving the mobo and PSU exposed.  The Power Supply is that whole whitish gadget on the right side.  Here is an image of the powersupply
(Note: It might appear slightly different, but this is the general idea)
Power Supply Picture
With the powersupply located you are going to need to unscrew it from the case, I hear that certain contacts can be charged even if its unplugged so be VERY careful.
With the powersupply out of the box look at the black connecter that you plug your power cable into, there are two pieces of metal that run down from the black connector into the board that the power supply is on.
Where these connect on the bottomside you should see 2 solder points, in my case these solderpoints had broken from tons of plugging and unplugging.
To repair this simply
Reheat the current solder or add a bit more to fix those joints.

If you need clarifying on these instructions please post away,
Good Luck,