At that age, I think they were still using the low oil level shut down switch. Very first thing would be to check oil level. All 3 of my 2800's (gasoline version of 2500) have required checking the oil with the stick _NOT_ screwed in, just resting on the edge of the hole. I assume yours would too. If you do this wrong, you'll be low.
The common issue with the small LP Onans is the regulator vent tube. Some insects are apparently drawn to the faint smell of LP, and love to build their nests in the tube. This keeps the diaphragm from breathing. It's more likely to happen when sitting idle, tho'. I've never heard of this happening when running. Onan finally started adding a foam 'sock' over the end of the hose, but IIRC that wasn't until sometime in the 2000's, AIUI.
Good luck!
Jim, "Mo' coffee!"