I have a 1993 coupe lt1 motor and the service asr light came on and after you turn the key off when you go to start agan it cranks but wont start until it sets for a while an the asr light goes out.

Anti Slip Regulation(ARS) is incorporated into the throttle, as well as the ABS. There is apparently something wrong with the system. It may be closing the throttle too far, and that would keep it from running.
You really need to have it scanned for codes to determine what the problem is, and where to start with correcting it. AutoZone will scan it for free if you do not have access to a scanner. Just be sure they give you a printout of the codes, and make sure they scan ALL of the systems.
hth

Welcome to C4VR, also!

The Service ASR Light came on in my 94.  Talked with the guys down at the Corvette Shop in Tampa, they told me to Top Off my break fluid and see if that worked before I did anything else.  I thought the fluid reservoir was full but I added some anyway, it actually took more than I thought it would.  I was lucky it solved the problem.