Hi Paul, is that a Vanguard or Intek engine - that is, a Briggs overhead valve engine? If so the symptoms are generally consistent with a very common problem.
The decompressor on those engines opens the exhaust valve momentarily about halfway through the compression stroke. This is similar to most other decompressors. However the Briggs one is very sensitive to exhaust valve tappet clearance adjustment, and it also may wear out after a while. If the clearance is even slightly more than specified, or the decompressor is worn out, the decompressor stops working and the engine won't turn over on the starter motor. So, first tell me what engine is in the machine, and I can tell you what the tappet clearances should be. Most likely the exhaust clearance of the engine you are looking at is more than it should be, and the engine will behave normally once you adjust it. However if the decompressor will not work even when the tappet clearance is at minimum, it will be time for a new camshaft.
If it turns out that the engine is a 33M677/0149-B1, the required valve clearances are 0.003-0.005" for both intake and exhaust, but this is different for each different engine size, so let's make sure we are talking about the right engine.
I haven't heard of the engine actually backfiring, we'd have to have more information to figure out what is going on there. If the engine is just about making it to the ignition timing point and stops rotation just as it sparks, strange things could happen - most of them not good for the engine.
