Dying when you release the start switch is a common failure mode on the 2.8 & other small Onans. It gets spark voltage from the battery while cranking, but has to self-generate it once the start button is released. Can be the voltage regulator, brushes and slip rings, or a much pricier rotor/stator failure. I think (not sure) yours is from after they dropped the low oil switch.
The Onan service manual will have a good troubleshooting guide if you're handy with tools and have a volt-ohm meter. If you don't have it, state all the name plate date, especially the spec letter, and someone here may have a pdf copy.
Jim, "I was troubleshooting, but ran out of ammo."
