"Advent" is NOT the manufacturer of the PC.
Who made it? HP, Compaq, eMachine.......WHO?
One thing you can try, if it's playing dead, won't cost you anything,
well, maybe $3.
With all power removed from the system, take out the little CR2032 coin-type battery.
Leave it out for at least 20 to 30 minutes. If you have a voltmeter handy check the voltage on the battery. It must be 3.0 vdc to be good.
If not at least 3.0 vdc, replace it!
Then after the above mentioned time, replace the battery, restore line power and try again to start up the PC.
I've worked on several HP computers that appeared totally DEAD, till I performed the above process.
Then they came back to life, good as new.
A 350w PSU in a desktop computer is usually NOT enough power. It's especially bad if it's a "Bestec" or "Codegen" PSU. I'd always opt for a 500w PSU to replace a 350.
The 350 on the PSU case is the momentary startup value, derate that by as much as 30% for the all-day operating value.
Good Luck,
Shadow