PIC24FJ128GA202 UART2 and UART3 not working?
I will share at least my experience with microchip, peripheral pin select and the UART maybe it will help you solve the problem. (cannot comment due to lack of reputation)

I once started programming on a dsPIC33F microcontroller with PPS. I thought that every pin was selectable for the UART. Well.. It turned out not to be the case. It took me a few days to find the problem in my system but eventually I found out that not every pin can have every function.

Tip: Change your pins and look very carefully if you have set every register accordingly to your application. Some registers have some kind of priority.

If I remember correctly the function closest to the microcontroller (pin diagram in datasheet) has the highest priority if two functions are set on the same pin.

Hope this helps.