Wish I'd seen this this earlier I might have been able to jump in. Have a VX-170, solid radio, but not as solid in testing gravity as one might think. My case had broken to the point it needed replacing. Yes having fine needle nose pliers to remove the nuts from under the knobs is helpful.
Replacement cases from Yaesu are no longer available, however, at the time I did mine the VX-270 (replacement model) case was available and it fits directly in. Only one of the silk-screen keys is mislabeled for an unsupported feature was the difference.
As for the rechargeable battery, if it isn't charging or working after charging it could be the pack is bad. If a rechargeable cell gets over drained it can reverse polarity. Yaesu has/had a battery pack you could put your own AA (NiMH worked) batteries in it, or run it empty and just run on external power.