2001 Chrysler T&C remote start

Installed a remote start about a month ago and uses a security bypass with the transponder key.  Been having an intermittent problem where sometimes it will crank but not start with the key but will start with the remote.   I always know when it is going to act up as when I leave the vehicle the door chimes are going off as if I had left the key in the ignition.  

My hunch is that something is goofy with the electronics and the bypass is not stopping the signal to the ignition switch and thus the vehicle is seeing two keys.   Has anyone ran into something similar before?    If the vehicle is seeing two keys will it allow the starter to crank but not start?   

This thing is driving me nuts as my wife has no faith in the vehicle and has taken to driving my truck until I get this sorted out......I want my truck back!!

Hindsight being 20/20 I would have went with a higher quality unit but the remote start is a Bulldog RS1200E and the bypass is a Bulldog 791.

I had a friend that asked me to install a crappy unit like that in a vehicle(beer was involved in the bribe after install).I had to replace the key/rf bypass with an Omega unit because it did the same thing as yours.It appeared that the bypass stayed on.

Transponder box was the culprit, finally got ahold of someone from the manufacturer and they said they would replace it.   

Between their wiring diagrams not being accurate, having to tune the radio in the unit myself so it would get the proper range and now the bypass going bad it certainly was not worth the few bucks I saved by buying inexpensive equipment.  What little bit I saved was more than eaten up by the hours I spent troubleshooting, tuning, trips to the dealer (thinking it was a vehicle problem) not to mention one pissed off wife who commandeered my truck while I sort all this crap out on her van.  (is loss of one's truck considered emotional suffering?)

On a more positive note, the manufacturer's customer service department was very helpful when I was able to speak to them......probably from lots and lots of practice!