If the switch is such that you can take it apart without too much
trouble, I'd try that (with the saw unplugged, of course). My "new"
10-yr old BS had the same problem when I first got it (power to the
machine, but wouldn't turn on). Fortunately (or unfortunately, as
magnetic would be nice) it was a simple double pole switch, and it was
a matter of taking it off the machine, rubbing gunk off the contacts,
and putting it back on the machine. Works fine now.
A quality minute with the switch and a continuity tester would reveal
whether this is your problem.
Hope this helps,