When the capacitor blew on my old Nu Tools lathe, I was really pee'd off. Then I thought . . . if its just a starter capacitor, spinning the chuck should get it going - and it did! AND, I could spin it backwards for sanding! So, when I eventually fitted a new capacitor, I added a switch that could disconnect it for sanding. Worked a treat!
The same trick would probably have worked with your saw, but spinning a multi-toothed blade to get it going - I don't think so !! #-o