Welcome to the the greatest forum in the whole wide world, 
(Thank you Marion.) i`m sure we can get you started on the path to trace your grandfathers story.
First thing to do if you have no documents or records of his service is to look on the NARA AAD (Access to Archival Databases) http://aad.archives.gov/aad/index.jsp and look for his Electronic Army Serial Number Merged File, ca. 1938 - 1946 (Enlistment Records)http://aad.archives.gov/aad/series-list.jsp?cat=WR26 That will give you his Army serial number & enlistment date with some other info. Having the serial number helps <sometimes> in getting records from the national records center in St Louis. Then you can file a records request online at E-Vet records, or you mail or fax a SF -180 request form that you can also get online.
There are 2 listings on AAD for Barnette:
"BARNETTE#WOODROW#G " from MECKLEMBURG county and
"BARNETTE#WOODROW#W" from IREDELL county , maybe you have another relative?
Let us know whatever help you need, and and enjoy your quest.