No your front lamps do not have to be grounded to make the back work.

I know this because I completely installed and tested the rear wiring before I installed the front wiring harness. The only thing I couldn't test was the flashers.

Possible issue is that the wire for tail lamps came loose from the light switch. You could start from there. Probably easier though to check for loose connections, damage, or ground issues starting from the tail light sockets and work you way back to the switch.

If you don't already have one, a wiring diagram will help a lot to understand the whole circuit as you work through it.