The click you here is probably the solenoid trying to engage the starter motor. When that happens, it is supposed to close a connection to provide juice to the starter, but in your case, that apparently isn't happening. I had a similar problem on our '83, and found that when I tightened down the post on the solenoid where the battery cable connects, the starter wouldn't work, but if I tightened the cable without first tightening the post, it would work. So you might just want to fiddle a bit with that connection, but DO disconnect the battery first!
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'81 GLT 245 W/245K; '83 DL 175K