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Okay, I'm going to change out the clutch (I'm pretty sure that's what is wrong). I was talking to a guy about it and he said that there is a clutch kit that comes with the clutch, a new pressure plate, and new flywheel, along with the clutch aligning tool.
Where can I get this? And, I'm sure I need a specific clutch, etc., for my '78. How do I know which I need?
You should be able to get a clutch kit at every good parts store.
IMPORTANT for the Corvette: Have a SPECIAL CORVETTE kit!!! The thrust/throw-out bearing on a corvette is lower than on other Chevy's! A parts guy who does not know will usually ask about splines (26 in your case) and size (10,5" I would assume with your car).
Check the starter bolt pattern - if the 2 9/16-bolts are in one straight line (crosswise to the vehicle), you will have the small flywheel (153 teeth) which only allows for 10,5" clutch.
If the bolts are positioned staggered (on further to the front of vehicle), you have the 168 teeth flywheel - this would then be 11" clutch.
But I assume that 10,5" is what you have (11" was only used on big blocks and high power small blocks like LT1 or L82).