the parts for this particular mower are fairly common on ebay, and as i have just rebuilt one of these i would say check your govenor springs, air filter and as for the diaphram gasket , turning the mower on its side should not affect it how ever it is worth noting that if your going to do repairs that require tipping this mower up or over it is a wise move to drain the oil and fuel as with this particular mower it causes problems.
Also the choke is located inside the carb tube and is a automatic choke hence the reason for the mower to have the two govening springs on it. and spark plugs usually are relitavely sooty.
CYBORG
September 2010