Although the problem may indeed be a hanging throttle cable, I'm inclined to think that the issue is with your TORS system. Most likely either a bad/damaged connection, a shorted wire up on the bars, or a faulty parking brake or throttle switch. All of these TORS components are mounted on or around the handlebars. If something were to start acting up (and this is very possible, especially on an older blaster like yours), you might have been able to jiggle the handlebars to keep the connection made. Until now, that is, when something finally crapped out for good.
As was already suggested, I'd just make life a lot easier for myself and defeat the whole TORS system with one swoop. TORS is a big fat Yamaha joke that serves little, if any, practical purpose. Just take the hood off your Blaster and unplug/remove the small, black box located on the upper right side of the frame. It will have 3 wires (2 black, 1 yellow) coming out of it. This is the control module for the TORS, and once you unplug it, the system is deactivated. Try your kickstarter again. I bet it will fire now.