2000 dodge stratus dies after 45 mins of driving

new issue battery is dead after sitting. constant humming noise heard from rear when charging to jump. yes, im aware of the usual hum of the pump when key turned to on. humming is constant key on or off even removed? curious if new relay could be stuck on?

took it to the shop and had a new battery put in. guy at the shop said it was fine. still humming and died while driving home. replaced original relay no hum but still dies after driving a while. thinking about replacing coil pack but tired of throwing money at the problem.

transmission sensor seems to have been the issue. runs a little rough at idle but doesnt die and not start. only other issue was rpm hit zero once but went back up like 10 secs later. this was during a 45 min drive in city so varied speeds 10-65 mph.