What is the engine model & type number? Date code would help also because
some engines were slightly different over the years.

One of the easiest checks is to remove the air filter cover and filter,
prime the carb and see if there is any fuel in the carb throat. If there is
fuel, then you have a problem with either a gasket leak or compression
and/or valve problem. One way to check that is to do the same as before but
start the engine. As the engine is running, slide a finger over the carb a
small bit at time so that you are creating a choke effect. If the engine
starts to stall, then you can rule out a fuel problem or gasket leak. If the
opposite is true, then look at those. This is also a trick used for other
types of engines too.

One thing that most people miss when servicing small 4 cycle engines are
the valves. The exhaust one being a culprit alot of times because of the
heat that passes by the valve face and either burning it or causing carbon
build-up. I'm not saying that is your engine problem but keep it mind if
everything else checks out ok. Many times Techs will change both valves plus
the headgasket when an engine hasn't been serviced for quite a while. One
bad habit that many people have is leaving an engine in a damp place with
one valve open. The valve stem may corrode enough to stick it open a little
and cause backfire as I've seen that many times.

Not that it makes a whole lot of difference, but I'm a Tech and if you need
any other info, I'll try to reply if possible.

Mech_Tech