It sounds like you had the starter installed professionally. If that's the case, the install itself along with the remote starter should be under warranty. In fact most installs carry a lifetime warranty, because if done properly the likely hood of failure is very small. The device itself fails far before the wiring to it. Of course remote starter usually has a rather limited warranty. But one way of the shop getting out of that lifetime warranty on the install is if they can legitimately claim that you tampered with their work.
In other words DO NOT ATTEMPT TO FIX IT YOURSELF. Not first anyway. Let them right the wrong like they should. It actually protects both of you to do so. If you can't get the work done free(not a warranty on install or whatever) only then get your own hands dirty.
I would guess that the switch itself is not the problem. But rather the new wiring to it. The splice. This may be a very simple fix. Wouldn't that be a nice change.