Electrical problem?? 2000 GTP

I’m hoping someone can help. To start off I put a new alternator on the car last week. Today I was driving around making several stops. when I went to start the car after the last stop it wouldn’t. I can hear the started clicking, so I know its not that, when I let off the key, the car has no power for a few seconds, then it comes back on and all the lights are dim, they fluctuate and eventually come back to full power. I checked my battery connections and they are fine, I wiggled the wires under the circuit panel next to the battery and played with the battery connections, and taped and wiggled a few other things. All of a sudden the car started I have no idea what I did. It worked fine for about 10 starts, then I was driving and the car shut off, it started right back up, then did it again 2 more times. Does anyone know what this is? Faulty battery? Coil?? I am at a loss.

check all the connections

Check the battery-to-car ground or you could have a bad pos battery cable.

Check THIS (http://www.automotiveforums.com/vbulletin/showthread.php?t=196432&highlight=positive+battery+cable) thread. I hope it helps.