I have a 1976 Corvette with a big block rear, 4.30 gears, spool, turbo 350 transmission.  I was driving it under normal conditions (pulling out of a parking lot) when I heard what sounded like a draging noise coming from under the car, like the drive shaft dropped down and was scraping on the road.  After stopping and checking under the car (nothing visible), I kept going and the noise went away.  As I pulled in my driveway (in which I lowered the gear from Drive to D2), the noise started again but much louder and seemed like it was actually slowing the cars forward progress.  I managed to get the car in the garage and jacked it up, trying to replicate the sound to find out where it was coming from - no luck other than once in a while it seemed like the tires would stop spinning, like something was binding them up.  Anyways, I put the car back on the ground and went to back it out of the garage and it stopped, almost like it locked up.  The car would not engage in drive or reverse, and when I put the shifter back in park while the car was running, it grinded just a bit.  We pushed the car in neutral back in the garage and have not touched it.  Looking for your input on what you think it may be (tranny - rear end?).  Thanks for any advise you can give me trouble shooting this problem.  

My instinct would be the transmission.  The TH-350 is good for mild applications, but high horsepower/high torque applications, like big blocks, will likely tear one apart unless it's been built up.  That's why any cars that ever came with big blocks and automatics were paired with TH-400's, even in mild big-block applications.  The fact that you stated it was grinding when it wouldn't engage drive or reverse also points to the transmission itself.  More than likely if you'd blown out your rear differential, there'd be a hole somewhere and a pool of fluid under it.

Now, since you've stated you have a big block in the car, you're probably not overly concerned about originality, so providing the transmission is the culprit, my personal suggestion would be to go with a built TH-700R4, or at least a TH-400.  The 700R4 will at least give you an overdrive gear to utilize, which with your rear gear ratio should make it a bit more streetable, and with the tall first gear, give you better launches too.  Keep in mind though that the stock 700R4 is just as weak as a TH-350, so if you go that route make sure you get one that is built to match or exceed your engine application from a reputable source.  And of course you can pick out a nice billet torque converter at the RPM stall of your choice.  

I'm confused, does your car have a big block, or the rear end out of a big block Corvette?  

Thanks for the responses.  It has a rear end out of a big block corvette.  It actually has a 358 sbc.  I am trying to get some input whether it was the transmission, gears, or maybe something up with the spool.  I don't know alot about drive trains, so trying to pick your minds before I start to trouble shoot it.  Apparently the transmission was rebuilt previously and beefed up, it has a 3500 to 4000 stall converter.  Don't know anything else about the rear, other than synthetic oil has been used, 4.30 gears, and has a spool.  I have looked, had it jacked up, etc, fluid levels are good and no leaking or puddles.  Thanks again for any suggestions.  

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OK guys.... I finally got the time to remove the rear cover of the differential of the Vette.  Along with numerous small pieces of metal, there are several large bolts that appear to have been broken off and were in the bottom of the casing.  Any idea's where all the larger bolts came from?  Thanks again for any idea's.  

Looking further into this tonight, found the bolts are the Ring Gear Bolts that were sheared off.  10 bolts in all were found in the bottom of the oil container.  Anyone have any idea what would cause this and how much damage may I have caused?  The gears when spun, don't look bad.  There are a few spots inside the casing where chips and pieces were broke off, Im sure by the bolts flying around.  Thanks for any opinions on this.