computer shuts down by itself

My computer will shut down when I first power up. I'll power the tower down, then power up. I'll have to start a new session. I'll go into e-mail, Facebook or Internet. Sometimes it will be OK, sometimes it will shut off again and I'll have to repeat it. If I go into one of the games and play it, then it doesn't shut off. Checked with cable company and they said all their hook ups were OK now. Initially, when the computer would go off line, the phone wouldn't have a dial tone but that seems to be fixed. Cable company installed new equipment but still will shut down once in a while. Then it will have flashing white stripes across the top of the screen.