'95 Z28 theft deterrent system problems

I have a '95 Z28 that exhibits some strange theft deterrent system problems.
*frequently, the keyless entry will not unlock the right door. The
actuator works fine when unlock is selected from either interior door switch. The left door operation is unaffected.
*Occasionally, the system will arm itself with either door and / or the hatch open.
*Occasionally, the starter will not crank with the key in the start position, and the security light illuminates momentarily in this condition. The starter will usually crank then if lock is selected on the keyless entry, and then unlock is reselected. If this fails to allow the starter to operate, it will operate if start is continually selected with the ignition key; as if there were a solenoid problem or intermittant open in one of the starter fields. (The starter is new and was not the problem.) Any ideas?
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