Dave,
It does have an OPC, part number 6C190-55515
Steve
I do have a B2910, which is physically the same as the B7800, but does not have an OPC so it is not the same.
Looking at the diagram Dave posted, your fuel cut off solenoid has both coils hooked in parallel, so they operate together, when the OPC energizes the (2) key stop solenoid relay.
Since we do not know the logic within the OPC, we can only assume the solenoid is either always energized when the tractor is running, or that it is only energized when the tractor is shut off, to cut fuel off until the engine stops. Has to be one or the other.
What I probably would do is first pull out the key stop solenoid relay and see what happened. If the tractor still does not start, this would indicate that the fuel cut off solenoid is likely energized to keep the tractor running, and deenergized to shut the tractor down. I guess you could accomplish the same thing by unplugging the fuel cut off solenoid if that is easier.
(Of course, simply checking voltage applied to the solenoid would also give a clue as to what is happening.)
With the relay out of the circuit, and if the tractor did not start, I would apply 12 volts to the solenoid directly, and see if the tractor started. If so this would prove the issue is not the solenoid and something else. And prove that you need 12 volts applied to the solenoid for the tractor to run.
Which would mean, either the key stop solenoid relay is bad, or the OPC is not telling the key stop solenoid relay to energize. The root cause could be a bad OPC or something going on in the switches feeding info to the OPC.
So after all that, what could the root problem be?
A bad OPC
A bad key stop solenoid relay
A bad fuel cutoff solenoid
A bad switch feeding the OPC information (8,9,10,11,12)
The clutch switch would only come into play if the starter does not turn the engine over, but it sounds like your engine turning over.
Try to get some measurements/more info and report back. OPC modules are expensive I believe so you don't want to buy one if you do not need it.
Hope this helps...
Also, you may find a B7800 workshop manual at kubotabooks.com for free or a small donation to the site.
edit: the key switch could also be the issue, but unlikely, since you already replaced it and it functioned until the issue reappeared. Also a wiring problem could be there, but one step at a time...