I use a remote switch and relay as well to save the NLA ignition switch. Here's my diagram.
http://members.rennlist.org/911pcars/RemoteStarter.htm
Might be similar to yours. Not sure what terminals the PO used. Since the relay clicks, you should be getting source voltage at the wire (30 or 87) that goes to terminal 50 of the starter solenoid. If the solenoid doesn't click, the solenoid is bad or isn't grounding correctly. If the starter clicks but the starter doesn't rotate, it could be the connection between the solenoid and motor (large copper disc) and/or the starter is malfunctioning.
Sherwood