BleepingComputer.com: once shutdown, won't boot up again

My computer is working properly UNLESS I shut it down and try to boot up again. When I do this I have great difficulity booting up again. I keep getting a never-ending cycle of the COMPAQ page, then the black Microsoft page, then the Logo page with the sound effect, and then the Log-On page. But the log-on page will not accept my password and it will not stay for very long until the cyble starts all over again.
I have done F11 to do a system restore and that will work IF I try it 8 or 10 times with different restore points and that has taken hours. I have tried StartUp Repair as well. Now I cannot shut my system down for fear that it will take hours to get back online.
Any suggestions are greatly apprciated!

Sounds like a failing PSU to me. Depending on your tech skills, I recommend you replace the PSU (Power supply), or get Compaq to do it.