Not going into gear

Had a dead battery for a month. Bought a new battery and replaced it. After three days of driving the charging system wasn't working and as I was driving the battery died. The mechanic replaced the alternator charging system and it works fine but then the transmission failed.
No reverse or drive but when you put it into 1st gear it gives a thud but then drives up to third gear. Fluid levels are all good.

Can this be a failure in the computer? Due to jump starting the car many times? Or can it be caused by anything we did above.

Before the battery died whist driving the transmission was fine. No issues or problems.