I'll answer your question in the last paragraph, but first, check those big "shotgun shell" fuses with a continuity tester, or even a wire, a flashlight battery and a flashlight bulb. They're impossible to tell if they're OK by looking at them. If a fuse is good, it'll conduct current. If it's blown, it won't. A bad fuse will prevent a good charger or good alternator from charging a good battery bank. I'm betting that that's your problem and you can just replace them (Ace hardware) and go.
If not, then I'd agree that you should first disconnect the switches. Something is wrong there and you don't want to start a fire. If you can do without power while you investigate, turn the switches to off and then disconnect both battery banks by removing all cables from the positive terminal.
Then check the "bad" battery bank. If you have a voltage meter, or the dash meter is OK, check the voltage compared to the nominal volts. A 32 volt battery bank will put out over 33 volts when charged and will measure under 32 volts when discharged. If you have a battery hygrometer, measure the specific gravity of each cell. If they're all roughly equal, the battery is OK, even if discharged. The hygrometer will show what specific gravity measure is charged (i.e.1275) vs. discharged also.
If the batteries are OK, then follow the cables from the positive terminal on the house bank to both switches. You may have a loose or melted lug or terminal or bad cable somewhere. The hard part is just following the cables. If something is bad, it's usually easy to see. Feel the connections for loose terminals too.
Then, if you're comfortable with electrical work:
If they're all fine, open the switches and see if they look OK. If you have them both set to "both" then both banks should be paralleled mechanically, but you said the parallel switch allows you to parallel them and it works to start the starboard engine, so thats strange. If it all looks fine and clean and the fuses, cables and terminal connections were OK, I'd still worry about the switches. I'm not sure I'd hook them back up if they can be bypassed.
Last, to get you home but probably not ABYC standards, it is possible to add a manual parallel switch, but it can be tricky to use. You can go to NAPA and get 2 short cables big enough (like 00 size for a 32V system) to carry house loads, but not starting loads, and with terminal lugs the same size as the parallel switch soleoid terminals. Then get a 75 amp (or more) automotive push-pull power switch (75 amps @12V = 28 amps @32V). Use the 2 cables with the power switch in the middle to make a "switched jumper" for the parallel solenoid for your battery banks. Be careful - these wires and terminals can't touch any other wires or ground...protect them well. Turn the switch on to use both banks for everything, and to charge the bad bank when running or charging, but NEVER try starting with the manual parallel switch turned on because it can't handle starting current loads. Also remember that if they're paralleled, they'll equalize over time so the good bank will charge the low bank until they're both the same charge state. That can be good or bad based on charge conditions.
If you're not comfortable doing this type of work, stop at a good marina.
Good luck,
Doug Shuman