May have found the problem. I pulled the blower switch and found that it had overheated to the point that parts of it were melted. One of the contacts had melted into the housing and was making no contact at all. I don't know if this was caused by the resister or not but I'm going to go ahead and replace them both. I didn't find any evidence of a short and nothing else seems wrong.

With any luck that will cure the problem. It may be that when the old blower seized up it caused the switch to overeheat if it was left on. Thanks to all for all the advice on this weird problem.