MacBook screen going black - now going to log-in screen

Hi everyone

I have a 2009 Unibody 13" 2.4 MacBook, and recently on OSX Lion 10.8 the screen started going black for no reason, the keyboard lighting would go out, then after between 2 and 10 seconds (usually) the screen would come back on.

I installed Mavericks the other day in the hope it would rememdy this, and to some extent it has. Instead of doing this every 1-10 minutes it is now flicking me out to the lock screen, asking for a password two or three times a night.

Has anybody got any idea what is causing this? My battery needs replacing, could that be the problem? Or is my video chip dying? Or some other possibility?

Many thanks in advance for any suggestions

Robsa.