Small Engines (Lawn Mowers, etc.): Robin EY28 back firing through carb, crank case, cam shaft

Question
I bought a Coleman LR4300 generator from a guy who said it had just set for along time and needed the carb cleaned. I cleaned the carb by taking it completely a part and dipping it in Berrymans carb cleaner for 30 minutes cleaning all the jets and passages out. Tried to start it and it would not start and would backfire through the carb. It did start and run fine at one point for about 15 seconds and then it stopped. After many pulls and many backfires through the carb it started again and ran fine for 15 seconds it once again just stopped. I tried to keep it running by shooting carb cleaner into the carb but it simply died and would not restart. It also does not start if you even put gas in the spark plus hole and try it, it just back fires through the carb. I checked the spark and it is strong, the flywheel key is intact, the valves appear to be moving up and down correctly. As I understand it these valves don't appear to have any adjustment other than removing material from the valve stem. The valves appear to have the correct gap. I did notice some one on another web site described the very same problem with the same engine. The carb bowl is full and the float appears to working correctly.

I have disassembled the engine and it appear to look like new inside to include the piston still having the honing crosshatch marks. The rings aren't stuck as I broke one taking them out, (where can I get a set for less than $80.00) The cam shaft also looks new and it doesn't have a compression release. I also get a fair amount of  noise (like a squeak but not a metal to metal squeak) from the crank case tube going into the squeak housing. I suspect the guy who sold it to me may have been a bit dishonest.

The complete engine number is EY2800YD25104618

Answer
As far a a price on the rings, i would be googling online also, so that won't help much.

As far as the backfire, if all else is as you say, I would be looking at the ignition, have seen a bad plug do that as well, even
though is showed good spark.  Many generators have a finicky low
oil shutdown, maybe look in that direction as well.

   Also make sure you don't have a sticky intake valve, sticking open occasionally.