Just cause the charger is good doesn't mean the battery is too, even if you check voltage on the battery that doesn't necessarily mean it good either, I would swap out for a brand new battery, and see what happens, you can always go right back and return the new battery. Or better yet if your battery is under warranty just take it in and exchange it. They may or may not test it and tell you if they think it's good, autozone for example will do this. I'd also check your main fuses that might prevent a start, so the ones on the relay you are soldering and some of the ones in the under hood fuse box. Also check your connector plugs going to the ecu and those relays to make sure they are all seated good and not corroded, unplug, visually inspect and clean if necessary and plug back in. I had a crossfire that had surface corrosion on a plug going to either the ecu or relays, it would start, barely but started with new battery, then ran like it had a misfire, and had no acceleration. Cleaned the corrosion and all was fine.