my macbook air suddenly started rebooting last ...

My MacBook Air started rebooting last week and then shut down. I managed to get it to reboot and no matter which browser I use, as soon as I attempt to go on line, the screen goes blank although the keyboard is illuminated. At one point it showed the battery discharged and on yet another instance, it showed 70% battery just as the screen went blank.

Resetting SMC could solve the problem.