Does your blaster still have the Throttle Override System (TORS) still installed and hooked up? Check the top of your carb, if it has a cap like most bikes (other than stock blasters and banshees), then it is removed and its not that. If there is a giant junk box sitting on top of your carb with wires coming out of it, that is the TORS/idle control mechanism. Check to see if the wires are still hooked into a connector that is then wired into the wiring harness. At the handle bar, check if there are wires coming out of the throttle housing that then go down under the hood to a connector and then into the harness. If all of these things are intact, then your TORS system is still hooked up and it could be malfunctioning. It is supposed to sense if the throttle gets stuck open. If the throttle gets stuck open, the TORS system will cut spark. However, it often malfunctions and thinks the throttle is stuck open when it is not, and then you cant get the bike to run. A good sign of this is when you kick the bike over, you get one spark but thats it. So it fires once, but then blurbles out and wont idle.
There are some other threads on how to disable or remove the TORS system. In a nutshell, you can either order a TORS removal kit from either Vito's for around $45, or Dennis Kirk sells a Moose Racing kit for around $65 that comes with an anodized trick looking carb cap and a stainless braided throttle cable. The Vitos kit just comes with a plain stamped carb cap and regular throttle cable. Both kits come with an idle screw kit, you have to drill out the hole on the riders left side of the carb and then tap it with the supplied tap, you then install an idle screw since the idle control will be eliminated if you remove the TORS control box on top of the carb. The other, less expensive (free) option, is to simply disconnect the cables coming from the control box on top of the carb, and then disconnect the cables coming from throttle as well. On the 87-02 models this is sufficient, but on the 03-06 models, the wires have to be cut and spliced together.