The next logical step is a cylinder leakage check, where compressed air is introduced into the cylinder through the spark plug hole and you listen for leakage at the intake, exhaust, and crankcase filler hole. Both vakves need to be closed, and the piston at or near top dead center when the air goes in. Put the transmission in 3rd. gear and lock the parking brake or chock the wheels to keep the crankshaft from turning. If, as you suspect, rings are the problem, you'll be able to hear air escaping into the crankcase by listening at the oil filler cap. Unless there's a big leak, I'd suggest driving it, and keep an eye out for blue smoke in the exhaust and/or excessive oil consumption.
Jerry