OK. First of all it's difficult, if not impossible to troubleshoot an issue when there is another known issue with the board left unresolved.
At this point it is impossible to say definitively whether or not the battery is causing the MIDI to malfunction unless you first rectify the Battery situation.
I do know on Kurzweils the MIDI output is set in the Master Preferences and if the battery is not keeping that setting intact it may be disabling the MIDI ports by default.
Secondly, MIDI ports on vintage gear was notoriously flaky and breakable by simply plugging or unplugging or reversing MIDI cables accidentally. MIDI uses a 5 V current loop which was not properly diode protected on older boards.
Here's some video on opening up a Kurzweil.
My advice is to either try and fix the battery yourself or else take it to a tech who will do it for you and troubleshoot the MIDI issue while he's at it.
And here's a link to a PC88 Service Manual...
https://www.google.ca/url?sa=t&rct=...l-no-sch.pdf&usg=AOvVaw2z2ii10UPT1DpeexSD6oW7
Hopefully this will help you out with this.
Gary