Start up problem

Hello,
I have always shut down my computer at night, one night it was working and I shut it down, the next day I get a screen with compaq across and 2 choices of what to do either f12 system boot or f10 bios, something like that anyways, I did not know what that was, I shut off my computer from the tower because I had no other choice, and I started it again and it worked fine, I had to turn on my computer twice for a long time, then one day it just would not get past the compaq screen I took it in they told me that nothing was wrong it and it started up just fine for them, when I got it home the same thing happened I had to reboot my computer more than twice sometimes it was like 20 times or more, then I finally saved some money and took it in to another computer place and the guy said there was nothing wrong with it and it started up just fine for him as well, I changed my monitor and keyboard same thing happened so I know it is not those, now it still brings up the compaq screen if I shut it down, which I don't it can take up to 30 or more reboots to get it on, I have pushed f12 for system boot sometimes it works sometimes it doesn't, it will at times give me the other option of press any key for additional options or something like that anyways, nothing happens no matter what button I push. now my computer will automatically just shut off and when it is working it will flash on and off screen not all the time but a good portion of the time, I have also had it do other strange things on the monitor such as it looks like the screens ink has run all down the front,(like your tv when the station is off air) but that only happened once. or when I am scrolling it will do strange things and mess up the words so I can not see them really at all. I went to do a dskck and when it shut down on its own I finally got it restarted again and it started with a dskck and then shut off, when I finally got it re started again it never did a dskchk again, this is driving me nuts, I always do a virus check using avast, I use adware, I defrag and clean up my computer, I do everything I possibly can to keep it clean. can you possibly give me any suggestions why this happens or something I can try to do ( I am wondering if it has anything to do with the power supply in my apartment? I don't know just a thought though. I have tried a different power bar and new power cords as well. I don't shut off my computer anymore.