Re: Computer doesn't turn on, power lights blink, could it be the power plug?
Sounds like bad power or an overheating component. Dust the fan assembly out as best as you can (quick SHORT bursts of air from a compressed air can are best, don't let the fan spin up too fast or you'll fry the bearings) - also listen for the fan. Does it spin on at all when you turn the system on? It should. If it doesn't, consider getting that looked at if you can't fix it yourself.
Bad Power could also be the cause of the system startup issues, or it could be a fried motherboard. Was the system working normally recently? How long has it had this issue?