Try a vacuum gauge on the intake to see if there's s big fluctuation. If a cylinder is missing, or there's a big compression difference, it will show up as a rythmic dip in vacuum as the bad cylinder tries to fire. If you're getting a lot of blowby from the crankcase, your suspicion about broken or stuck piston rings is probably correct. Do a compression test, or a cylinder leakdown test to confirm the problem. With the crankshaft locked and a cylinder at top dead center on the compression stroke, put air pressure into the cylinder through the spark plug hole. listen at the intake, exhaust, and crankcase filler for air leaks. Repeat for all the cylinders to isolate the problem hole.
Jerry