Hello, I have a 2010 Infiniti G37S Convertible 7AT.
Miles - 55,000

I'm having issues starting the car and the relearn process. My car has recently been having issues misfiring and starting in general.
The start of it happened after a spark plug change. Car would misfire at only high speeds. The spark plugs are pre-gapped and the correct plugs for my infiniti. From the misfires I would get a Cam pos sensor bank 1 failure. Replaced Cam pos sensor. Issue persisted. Cleaned MAF and TB. Changed air filters. Did the 3 relearn process after cleaning throttle body. Also found a vacuum leak that I repaired. Had no issues for a couple of days. Then misfires started happening again after about 3 min of driving not at high speeds. Got error P0340 for cam circuit failure, found out that my battery was defective, changed battery, checked the fuse that I think is for the cam sensor and it is not blown. After changing battery car did not want to start. Car will only start now after doing the accelerator pedal released position learning. After I get my car to the correct temperature in order to now do the throttle valve closed position learning the TB's make the right noise for a successful relearn. After this step the car does not start back up again, and I would like to be able to start it in order for the car to be hot enough for the third relearn procedure (idle air volume learning). But am stuck in a loop since car doesn't start back up after second relearn process.

Unknown if the car is still misfiring since new battery. Code P0340 has not shown up since battery changed but also has not been driven enough since.

Note* After first relearn when car is able to start car idle's is at correct RPM however in D the cars idle is at 500.
My car is also bone stock.

Thanks