Hi Ben, welcome to Outdoorking.
There are three elements in getting an engine to run: spark, air/fuel mixture, and compression. If it doesn't run, at least one of the three isn't happening. You have said you have spark, but you have wet plug and fuel coming out of the exhaust. Unless you are wrong about the spark, the explanation that fits the symptoms best is flooding.
Flooding with chainsaw-type carburetors is usually due to carburetor settings or carburetor diaphragm. If your saw is really old and sick it could be that it just has no compression left due to bore scoring and ring wear, but you said it has good compression. Hence, if you are sure it has spark, you need to overhaul the carburetor. The most common single cause of flooding in that style of carburetor is the metering lever being set too high. This happens after an amateur has tried to fit an overhaul kit and has failed in his/her efforts. The next most common cause is dirt under the inlet needle valve. Neither of these faults necessarily requires replacement of diaphragms. However you may need a kit anyway if the existing diaphragms have been badly installed.
If you tell us what make and model of carburetor your saw has, we can try to find you a free on-line manual which tells you in detail how to overhaul it.
