QcAk :
I have a new PSU that I can replace the old one with. I hope that's all it needs...
Before you replace the PSU, reseat everything like I said.
Also, the button on the computer case may be broken or not working properly. Take off the front cover of your case and see if there is another button underneath the plastic button on the front cover. If there is, try powering on the system that way also.