@bbullsj, I don't know your skill set or your understanding of electronics, but honestly, you might be better off just having it serviced by a pro.
Without a schematic and proper test equipment it may be very difficult/nearly impossible to fix. Not to mention you and the forum may need the patience of Job.
My knowledge is limited, but here's my take on where to look if you still want to tackle this:
The encoder has two outputs seen in the traces seen in the blue circle of the (one) picture you posted.(as well as a third ground pin.)
If you follow them they likely go to a interface chip that decodes the volume encoder position and then likely outputs to a op amp chip that changes the gain (volume) to the final amp. There may be a separate ic for the digital display, or they may all on one chip.
You could start by writing the numbers on the ic's you think may be related to the volume circuit. A google search of them should find out their function.
With no schematic you'll likely need to draw out the component connections by following the traces on the pcb like a roadmap until you can understand how it works.
You may get lucky and find the problem without much ado, but if they are surface mount (smd) you will of course need hot air soldering abilities to replace them.
