I have a 1999 rodeo, v6, 4x4 with automatic tansmission. The engine would start but will not turn over. The mechanic seems to think it has to do with the alarm. However, there is no chip built into the key

I dont really know about this one unless I heard what was happening for myself. Sounds to me though that it may just be that battery. Either a bad battery or just a bad connection but jump on me if its something else. Your mechanic should know better personally.

Not a battery issue because we jumped started it but no luck.

I dont know... bad starter???

Check your ground wire bolted to the passenger side of the motor for good connection and connections at the starter.I just replaced the head gaskets on mine forgot to tighten this bolt and same problem. If all the connections are good it could be the starter. If it is the security anti theft, you can remove the 10 amp fuse and try that. Good luck.