I believe that the ignition switch is a common problem on these vehicles, I have read many folks having issues w/ the contacts. I bet 4Crawler.com has info on it.
Also, did you get an AutoZone reman? Apparently they are terrible, many people have issues w/ them dying fast. I'm on my 3rd one now, I'm fairly sure the 3vze uses the same unit as the 22re, what I have.