I have recently been having problems with my battery draining for unknown reason in my 77.  It will start up fine however after about 6-7 starts, the battery would be dead.  I had to jump it to get it going again.  I started by replacing the battery.  With the new battery, the problem has continued.  I'm thinking that I must have a bad ground/short or something that continues to pull power of the battery even when it is sitting and the car is off.  I have had problems with my tail lights and turn signals not working properly due to a bad ground.  Sometimes they work and sometimes they do not. I am wondering if this has anything to do with it.  Quickly, on a side note, when I have my headlights on, the turn signals do not work however when they are off, the turn signals usually work.  Any ideas as to why this is happening.  I cant begin to understand why my battery is draining.  Could it possibly be that I need a new alternator.  My volt gauge in the car is reading that it is good.  Thanks for any help, I appreciate it!

To me it sounds like you have an alternator problem or a bad battery. If it will start after setting overnight it doesn't sound like a short to me. When you say after 6 or 7 starts the battery it dead...that sounds like a charging problem or a bad battery.
just my 2 cents

Thank you....I may have a bad battery but like I said it is brand new and I made sure that I slow charged it before I put it in.  I will have to double check my alternator now.  

Maybe a voltage regulator, have your alternator tested, if your battery is charged and after a while it's dead something is not charging..

If your alt. is charging, and your batt. voltage is good, it could be your starter solenoid getting hot. I've seen them act that way, and after it cools down it spins over normal again. A new solenoid might be the cure.

I gotta say it sounds like a bad connection somewhere.

Even tho the alternator may be "charging", and the battery is new, if the voltage isn't getting from the alt. TO the batt, it won't charge it. Check the ground cable from the battery that goes to the frame, underneath the battery box. Also check the ground cable from the frame to the engine, usually on the passenger side, at the engine mount area.
If you have a voltmeter, put it on the battery, and see what kind of voltage is there with the engine running. If you see anything less than 13 volts, there is a problem. Then, put your voltmeter + on the large terminal of the alternator, and ground the other lead for the v-meter to the engine. See what it has there. If there is good voltage(14.5v, engine running) at the alt., but less than that at the batt., then you definitely have a bad cable connection somewhere.

A bad connection like this can be "masked" when jumping the car off, because you're putting more amperage thru the cables, and sometimes that allows a bad connection to make contact temporarily.

The turn sigs not working when the headlights are on is also going to be a ground related issue.
I don't envy you having to trace all these gremlins down!! With the Corvette needing practically every single electrical component to have a dedicated ground, it can be a major PITA. Sometimes, tho, a LOT of different problems can be traced to one single, bad ground/connection. Don't give up on 'er yet!

Thanks again for all of your useful and helpful information.....I'll let ya guys know what I figure out!

I will have to buy a new alternator as this seems to be my problem.  As far as amps on a new one, should I get a 42 amp, 61 or 63 and what are the main differences besides the price.  Thank you!

If you have A/C, go with the 63amp...
Prices shouldn't be that much different.

Thank you!