Having the same issue, left me stranded at work at 7 am after a night shift. Changed with new battery and still no start. Local parts store says old battery has 530 of 730 CCA's and needs to be replaced. Haven't tried charging new battery to rule out a crappy new battery. Dealer thought it might be the key but neither key works, so that can't be it. Will be trying the relay swap and crossing my fingers, otherwise on to my shop to check on the starter/connections and hoping it's that simple, cause computer swaps and chasing electrical gremlins *shudder* won't be fun.
If anybody has a cure or has fixed similar pls post up. My lights/accessories all work, dim down when trying to start and I get a click, but no crank. Tried mutliple times to play with shifter in case it was neutral/park issue, won't start in neutral either. When it finally did start I had the key turned for a couple of seconds and it slowly started to crank and finally fired. Drove it home 15 min, shut her down and she started 3 times with no problems. Came back an hour or two later and no start, same thing. We had a cold snap here but it's recently warmed up, around 32 degrees F. Lots of salt on the roads, although I did get a rust proofing done a couple of months ago.
Help pls or my wife will kill me for buying a Hemi (05 GC) even though she likes the power