Well Pete, that's a remote that's less accessible. I'd check the solenoid wiring and function. Disconnect from starter, connect battery. Check for voltage at the solenoid starter terminal with key off, on, and in start. Obviously, it should only have voltage with key in start position. If it has voltage when it shouldn't, disconnect the low current(smaller) wires and check. If voltage is there, solenoid may be bad and always on. Make sure all wires are connected correctly.
