For the sake of diagnosing the computer don't connect to a power bar plug directly into the wall outlet . There are several things that could be causing this issue. Start by disconnecting anything connected to the computer except for the keyboard mouse and monitor .We'll start with a static discharge and ram diagnosis
1. Disconnect the power cord
2. Hold down the power button for 30 seconds, then release for 30 sec and then hold down for another 30sec
4. Plug in power
If this causes no Joy try this.
Remove memory and reinstall one stick at a time, if there are more than 1 DIMM of RAM, try each stick in each slot one at a time to see if the memory is ok and to determine if one of the memory slots is bad.
if there is still no joy then we'll move on to disconnecting the hard drive and the CD or DVD drive . If you haven't figured it out by now you should be inside you computer . Just thought I should mention that ;-) after disconnecting the hard drive and CD or DVD drive power on the computer you should get a boot then it should tell you theres no OS. If this is the case plug in the hard drive only and attempt to boot again if it boot here then the optical drive was the issue . If it wont boots then the hard drive may be faulty. However if you don't get anything at all you should look at replacing the power supply. Once you've tried all this contact us again through this post and let us know the results and we can go further into the diagnosis