Hi @kheath56033
Here is the service manual for the camera that may help.
It has a disassembly procedure sequence diagram that will allow you to disassemble the camera so that you can check if the battery terminal connectors on the SY1035 board are still attached and not broken free etc - see p.4-1 & p.4-2 (p.16 - p.17 of 27 pdf numbering)
As to why it is not showing that it is charging, it may be that since the battery only function isn't working as it may be "not connected" then it it won't show any charging as no current can flow to the battery to charge it when the charger is connected, but this is just a guess.
Here's the ifixit Sony Cyber-shot DSC-W830 guide, that may also help.
crwdns2934105:0crwdne2934105:0
crwdns2934113:0crwdne2934113:0
crwdns2915270:0crwdne2915270:0
crwdns2889612:0crwdne2889612:0
1