RL,
Shar and Hipshot are right on the money. If your great uncle's name began with one of the listed letters you may not be able to recover the complete record. What they will try to do is furnish whatever information that might have associated with his VA benefits. At times this can give you a unit, dates of service, and service number.
His social security number is easily obtained from this site. In fact you can use this site to find out all sorts of information on relatives who have passed away.
http://ssdi.rootsweb.com/cgi-bin/ssdi.cgi
Use the advanced search.
This will also give you his date of birth, place of birth and date and place of death.
I have checked records for winners of the bronze star in the past and there is no central data base for the information. Your best hope is finding letters he had sent home during the war, or determining his unit. If you have his unit there are several sites you can check to see if there is an alumni site. I would also check his local VFW and other veteran organizations he probably belonged to. To use the Bronze star on his VFW hat or uniform he would have had to provide proof of award to the post. Just some thoughts from a person who spends alot of time delving into such pursuits.