Battery dying on 85 Vette
 

My battery drains overnight and there are times that it is fully charged but when you turn the key, you get a loud click and everything goes dead. Any thoughts?

The loud click and everything goes dead sounds like a bad connection on a battery cabe. Could be either end of either cable. A battery on it's way out will act like yours,or if you;re certain the battery is good,pull all the fuses and replace them one at a time until you find the culprit,then fix whatever is shorted or grounded. Good Luck!
Ron

Check your alternator, make sure none of your cables are broken or cracked. Had a similar problem on my 86.