Have you tried removing the ball of the mouse and cleaning the rolls ?

With the ball removed, you can move the rolls with your fingers: this should move the cursor if the mouse is not broken.

To make sure: check for bend pins on the mouse connector and clean them with Isopropyl alcohol.

The movement of the mouse has nothing to do with the connector you resoldered on the Analog board, it's just a coincidence.

There's not a lot that can go broke with the mouses.

If nothing from above helps, you'll have to open the mouse and test the cable; it can be a wroken wire in the cable.

Greetings from Belgium