I have Compaq Presario S4000V, FP 15 Monitor.
Highspeed cable modem.

Lately my screen turns black with tiny white lines running horizontally at startup. Then it goes off by itself. The only way to get the screen back on is to use the monitor button, computer button or surge protector button.

Hello pcdr1968,

Welcome to PCHF.

There's little much you can do if there are any hardware problems with the monitor itself. Confirm that it is the monitor causing this issue by testing out another - possibly a friends. It's normally cheaper to simply replace the monitor than it is to try to get these fixed, as most of the components are generally integrated and not cheap to replace.

Does it sound like the monitor is the problem?
Or is this the computer?

I rebooted again today. The screen came up black with tiny white lines again, then went off. The only way I can get it to come on the right way is to push the surge protector button, monitor button or tower button.

If you turn the monitor off and back on again? - it does make the monitor most likely.

Now sometime when I turn it on the screen starts turning white. The white grows and covers the screen.

Yep, definately monitor.. lol