[RIP]

Sounds electrical rather than mechanical. Also sounds like the transmission has detected a failure and has gone into what is called "limp mode" meaning the transmission does it's best to stay in second gear to prevent excessive speed, therefore more damage. Are you seeing a service engine light? The OBDII fault detection system will store a fault code and light the light indicating a problem...in most cases. Some faults will not make the light come on. Recommend you do the "key dance" to check for codes. Better yet, go to Autozone and have them read the codes with a scanner. It's free and more thorough. You may have to visit your dealership or a shop to get even more specific transmission codes.

Why has this happened? "Clean" electrical power is essential to TCM and sensor function. Just a theory but, in the process of breaking electrical connections at the alternator/battery you may have created a spike that effected the TCM or one of the sensors it uses or a sensor and/or it's circuit may have been physically damaged in the process.