My MacBook will not stay on

My MacBook (May 2010) will not stay on. If I turn it on it will try to start up and then shut down. If I play with the cursor buttons it will finally load up and then come up with the dialog box (as if I had hit the power on button) and ask if I am sure that I want to shut down. I tell it cancel and it stays on for 15 seconds and then the dialog box comes up again. As long as I am doing something it will stay on. The moment I stop the dialog box pops up again.

Sometimes it will start up and shutdown and keep repeating until the battery goes dead, even after I close the lid.

I have tried resetting the System Management Controller by holding down the shift-option-control & power on button. That KILLS the machine for 2-3 days. Then mysteriously it will be able to try to start up with all the old symptons.

Of course, it is out of warranty. Anybody know anything else to do?

Thank you,