Sounds like the starter solenoid is stuck/bad or for some reason your remote-start wiring is giving some extra juice to the starter. I would also change or switch the relay (with an identical relay in the box) just to eliminate the relay. Switching relays along with a new starter should cure everything. If not, look at the remote wiring or temporairly disconnect it at the starter when you install the new starter just to see if it works fine with just the key-switch. Then re-connect remote start and cross fingers.
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Rick
