A shop that installs alarms would be able to hunt down the problem also. The dealer will rip you off and then tell you it's not a factory alarm system so they can't touch it. You have several options though. You can buy a factory alarm system from Bav Auto and install it yourself (they're easy...) or you can buy one of the Stellar alarms that also just plug into your wiring harness behind the glovebox. There are several how-to articles on alarm installations for the E36 available on the web. I like this one: Keyless Entry/Alarm install E36
. But for the money you're gonna spend to have the dealer look at it you could install a really nice aftermarket system that's plug-n-play yourself. That's an aftermarket FOB you have there anyway.
You're looking for this plug behind the glovebox.....