I had the same problem with my Sears 31510961 saw.
I could not find a replacement after extensive searches. Finally, I disassembled the handle and cleaned all around the switch and the switch itself. (The red safety button top pops off easily to really get at the switch.)
That did the trick...pretty easy, too.
If no luck there, bring to a fixit shop with an older owner....amazing how these guys can fix things. Good luck to you.
Donald, June 2008