Go through all the connections with a multimeter, especially around the bad vias. if the via checks open circuit, just run a wire through it, clean back the solder mask on all the traces leading up to the via, and solder the wire between all the connections, and run it through the via. fill the via with solder, as the wire will help carry it down, this will allow mid-layer connections to repair itself. Ive done this alot on water damaged circuitry. works fine. pick up a roll of 30guage insulated wire at ratshack to complete the repairs.

Sometimes the via may already be filled with solder, just recharge the solder with some fresh solder, and pull it out with desolder wick/braid, (ratshack), and then perform the repair.

I have fixed relatively modern factory radios this way. I had a GMC radio that the VFD tube display had died. turns out one of the via connections behind the big middle power button had open circuit. (fun to find). I work at and help run one of those "fix it everything" shops, and its something I have grown accustomed to.