I would still check the new battery. Most batteries are stored dead and then quick charged on the vehicle. However, since alternators only put out say 60 amps an hour you would have to drive you ram 10-12 hours to get a full charge, and thats not including juice to your accessories.
As far as oil I always run Pennzoil full synthetic 5W-20. Summer time with the truck loaded for long hauls I'll up it to 5W-30. The oil should be 5 weight though. The filter I tend to use STP or Fram. I read an article that the two are the best and from the last time I was in Autozone I observed metal flakes in 80% of the stocked Bosch filters, like it wasn't cleaned after machining the threads. Some of the Fram looked like the canister warped or crushed the cartrige when they were pressed together. Which sucks because I was always loyal to bosche and fram.
These days I buy my filters in gross from Summit and my oil from Wal-mart. There jugs of full synthetic are $25.00 and at Oriellys or Autozone about 45.00. Summit will alway demand higher quality in manufactured parts versus the chain stores recieving defects.
Side note. My truck wasted its rear gear sometime back under warrenty. The question was raised that I never changed the rear gear fluid. When I was at the dealer I called autozone to see if they had my record of purchaseing Lucas gear oil about two months prior and they said no. I called summit and the said yes from over two years prior. Summit then faxed the reciept to my dealer and it was then submitted to chysler under warrenty that day. Which saved me from running.
I would be patient with the noise, even though I am sure its like a festering splinter. I would just keep trying to isolate it in the engine. If it doesn't increase or decrease with RPMS then you know its not rotating parts versus secondary components. Worse case senerio just tell everyone it the supercharger making that noise.