Open the Side of the Case and look at the CPU Fan (its a large Heatsink with a FaN attached to it about 2/3rds of the way up the case). Check it this attempts to spin up when you power the PC on. Also listen for the fan in the power supply (top right).
If you get one Spin for a second or so, or nothing at all i would say its your Power Supply is gone. You could replace this yourself if you feel confident, only a matter of taking note of cables etc or take it somewhere.
Average £ for a PSU is ~£25 expect to pay £40ish for it supplied and fitted.
Phil Roberts, July 2009