Nothing but clicking when starting

[82 GT]

Ok..where I'm at so far:

Replaced starter last week and everything was fine until Friday nigh.
When to start car an get nothing but clicking. I have fully charged battery. Car starts when push started but not when jump started.

Here is what I've done so far:

Cleaned battery posts and installed new terminals
replaced starter relay on fenderwell
made sure battery was good and even switched to another one

Here's the weird part: When I swapped batteries, it started right up so I shut it off again and tried to restart and got nothing but clicking from relay again! I'm thinking(and hoping) that maybe it;s a lose connection somewhere. Today I am going to check all the grounds and their connections. I'm also going to see if the headlights dim when I turn the key. That should tell me if the starter is hung up at all

Is there anything else I may have missed or could be bad?
I'll keep you posted

I also forgot to mention that this is my '88GT (5spd) car and not the '82GT in my signature below.