This situation is a good reason to do a "cylinder leakdown check" before tearing the engine down. With the piston at top dead center with both valves closed and the crankshaft locked by either putting the transmission in gear and setting the brake or locking the flywheel with a set of vise grips, put air pressure into the cylinder through the spark plug hole. Repeat for all the cylinders. Listen for leakage at the carburetor (intake valve), the tailpipe (exhaust valve), or the oil filler cap (piston rings) Bubbles in the radiator indicate a cracked head or a blown head gasket.
Jerry

"It is better to be silent and be thought a fool than to speak and eliminate all doubt!" - Abraham Lincoln
Cringe and wail in fear, Eloi- - - - -we Morlocks are on the hunt!
There is nothing noble in being superior to your fellow man; true nobility is being superior to your former self. - Ernest Hemingway
Love your enemies and drive 'em nuts!