The clicking/tapping could be a bunch of things (injectors also come to mind). The valvetrain could have gone south due to lack of oiling, but the "sludgy" nature of the oil raises other questions. A blown head gasket can cause a leak between coolant and oil passages. Was the coolant clean? Up to level? How recently had the oil been changed? No oil can cause an engine to seize, which is somewhat consistent with the shut it down then froze totally.
The other question in my mind is that the ticking is consistent with reported water pump failures, which seem to be the number one cause of engine failure on this board. Lack of cooling allows metal to expand, and can cause rotating/reciprocating components to weld togethor, freezing a motor. Its possible that you had an oddball failure (warped head/blown headgasket) of its own accord, or a problem with the previous oil change, but if the coolant is clean, try pulling the water pump belt, and turning the snout by hand. Loose shaft? Funny sounds?
If the engine heat seized (rotating assembly will not turn, then a new short block probably is the best route. The fact that it wouldn't turn over after the problem is not really consistent with a valvetrain problem (bound valvetrain can bind the crank through the cam chain, but the cam chain sprockets have keys which are supposed to shear). I would expect louder noises if the valvetrain bound but the keys did not shear.
If the water pump is trashed, document the daylights out of it, because the number of reported problems is starting to sound like a class action, which could help in the long run.
