power up problem

Computer is a 2-3 yr od HP slimline using windows 7 64 bit.

Problem is after normal shutdown it will not power up again unless unplugged for 30 secs. or so then it may or may not power up again. If left off for a few hrs or  overnight it powers up normally and runs ok forever. always ok if just restarted.

I am only basic computer savvy.  THANKS