They will not turn?  The other strange thing is that it will still bog down with the engine running and no drive shaft.  It did appear to have 1st, 2nd, 3rd and 4th.  But when you put it in reverse the shifting plate is not moving.  I hope I don't have to purchase a rear end and transmission. 

First, verify that the transmission is in neutral. Use a wrench on the linkages underneath, and position each shaft in the center of it's travel. If you get the front two shafts in the center, even if the trans is stuck in reverse, it should no longer bog the engine down. Be careful tho, and do not rev it up without the driveshaft connected to the trans yoke.

For the sound of it, you have two separate issues, but for both the trans AND diff to lock up at the same time is just too weird. Were there any strange noises before this all happened?

Joel Adams
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"Money can't buy happiness -- but somehow it's more comforting to cry in a CORVETTE than in a Kia"

Update on this Corvette.  I have taken the 1/2 shafts off of differential.  I can now turn the wheel hub.  When I grab differential you still can't make it budge.  I have 5 bolts to go to drop it down to see what is going on in the rear end.  I am wonder if the axle locking pin has slipped off and gotten into the gears.  Well anyway I will tackle the transmission after I get this differential turning.  

Yes, you need to check the shifter levers on the tranny.  Make sure as Adam said, that the levers are all pointing straight up and not in a forward or aft detent.

Okay everyone thanks for your inputs.  Here is what I found when I opened up the rear end.  I had lots of bolts sheared off of the big pinion gear on the back side.  What is your take on that.  I know we rebuilt the engine and tranny but I can't believe it produced that much more horsepower.  Anyway would you rebuild this one or just go ahead and find a good used one and hopefully it would hold up.  Not to sure a tooth might not be chipped as I still can't turn the wheels I see a few more bolts down in there.  Any suggestions would be appreciated at this point.  Thanks again Dean

In my opinion, it would be best if you called Brian Bair at his business and see if he can take your old one and trade it for a rebuilt one from his shop. That is their business. Corvettes and suspension. He may even have one that would be CORRECT for the numbers aspect if you want OEM status. 

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Is the transmission still locked up?

1973 L-82 4 spd

Trying to get someone to rebuild the differential or finding a replacement then it will be on to the tranny.  If I had to guess I think it's still in 2 gears.

My Guess, is your trans problem is shifter related. Take the shifter rods off, and place the attaching plates straight up and down. Then try to turn the output shaft. Another guess, is that the trans locked up between shifts on the road, and the rear took the bulk of the abuse. Trans was tougher than the rear. IMO!

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Okay I need a little more help here.  I did finally manage to get the rear end completely rebuilt and everything turns.  Well when it was hooked back up to the drive shaft I couldn't turn it anymore.  I figured it must have been in gear.  I crawled back out from under it and just my luck it was in neutral.  Made me sick.  So then I got the granddaughter out there to go through the gears for me.  I saw the outside linkage work.  I saw the long inside linkage work.  I told her to put it in reverse.  The small linkage did not move but the one closest to the tranny moved.  So I am almost positive everyone is correct that it is in reverse and another gear.  Tell me again exactly in laymen terms what I need to do to get it out of gear and into neutral.  Does it mean that the transmission is bad (was rebuilt last winter in FL) or is the shifter linkage is bad?  Need your expertise to finish this baby or I will have to disconnect the drive shaft call a wrecker and take it to a garage which I don't want to do.  Come on now I know you can help me.  Where do I look for these pins?  HELP  Thanks again Dean

Finally got there and figured something out.  Got the rear end rebuilt after the Positive Traction bolts seared off. On to the transmission.  I didn't understand until I kept reading and rereading the post about the put the levers straight up.  I finally took off the bolts and low and behold there they were.  I took a wrench and changed them to straight up.  I move the reverse one forward ward since it only had two ways in or out.  Not sure about that one.  Got back up there started it up and bang I had wheels moving in 1st, 2nd, 3rd and of course no reverse.  Do I need to move it back to straight up and then put the linkage back on to make reverse work?  I at least know I can drive it to a garage if I have to.  It took me awhile but I almost have it all fixed.  Also does anyone have any sliders for a 75.  I was going to replace the seats in this car and the boy didn't like them.  I was lucky to have sold them but messed up and gave away the sliders.  I have a pair but they are to short.  Thanks again Dean!