New battery installed, now engine light on and hard to start.

I just bought a 92 plymouth with the 2.5 engine. It runs very nice, but dealer sold it to me with a weak battery. I take it to autozone to test it, diddo, battery weak. they put in a new one. I pay for it and jump in to leave and now check engine light is on. I went out and found one of the main leads to the possitive side unplugged and the temp plug is out. I put them both back in and go back in to start it. Now it takes forever to start. and I find no other plugs undone.
So this same car jocky checks the engine codes, now its showing a code 22, coolant temp sensor, 44, fj2 voltage present at controler failer in the computer, 55, problem with distributor syncronization circuit. and now the fan runs full time.
I really dont have money to throw at this new development. and autozone assumed no responcablity. HELP!:rolleyes:

How have you fared? I'd double check all battery connections, clean and
retighten, also check lead at engine ground and positive lead at starter.
As far as temp sender, when unplugged the fan will run continuously. This
may also cause hard starting as computer may think engine is warm. You
can check resistance of sender. Resistance should decrease "I think" when
temperature increases. Hope your back on the road.