Yes I put a thin layer of the grease on the terminals. I can take it off and clean it out. I cleaned the wires very good and looked up the cable cover to make sure nothing was left.
The interesting thing is that the "dead" behavior of the car was like it was before switching the battery out. However, the terminal was a MESS. It hasn't done it again but I do for sure need to re-tighten the terminal so I will clean off the grease and reapply. I was following instructions that were given to me when my truck battery was replaced. hmm.
As for the gauge of the wires? Not sure on that one.
While I was working on my stereo project, I installed one of these quick disconnects on my battery terminal:
I used it so that I could quickly disconnect and reconnect the battery when working on all the electrical. I noticed that it seemed the connection was not very solid. This caused some flickering in the DIC, and twice, suddenly went dead when parked for like 15 minutes. All it took was to pop the hood, and jiggle it a little, but it definitely was an iffy connection.
I removed it and ended up using one of these as my permanent solution after the install was completed:
As a result, I basically cut the end off, put a terminal on it, and it's now bolted to one of those 3 bolts. I have a 4 gauge AWG coming off that that goes to a 4 farad capacitor, then a distribution block. I've left the 3rd opening as a temporary/test/etc terminal.
So that's why I keep insisting on something pushing/pulling on the terminals a little with the car running, and see if that causes any odd electrical behavior. I've seen it before with a slightly cracked connection to a battery terminal, and from failing cells within a battery before (would put out 12V, and then under 10V at times when one cell failed). I have never seen too much dielectric grease cause a car to not start. But hey, looks like you're going to address that anyways. And don't go nuts tightening the terminals. If you can't move the terminal, it's tight enough. So many people damage the battery terminals from over tightening the terminal clamps on the cables.