Windows server 2012 essentials GPO AD/SYSVOL MISMATCH

Problems with Swing Migration usually center around AD replication and the NTFRS service not working correctly. On a SBS server, which is typically stand-alone and doesn't replicate anything, these problems can go unnoticed for a long time with virtually no ill effect - until you add another domain controller into the network then the synchronization issues suddenly come into sharp relief. Check the event log for any problems with NTFRS, you need to hunt them down and eliminate them all, or you will never be able to swing.

Once NTFRS is working, I would try to use the Group Policy Management Console on the original SBS server to delete the policies. Then replicate AD with the policies already deleted to your new server. It's no good trying to just delete the files, the items need to be removed from Active Directory. Jeff Middleton at SBS Migration is a fellow SBS MVP and he is very good at sorting out these problems, he's seen most of them before. Use your included support incidents or buy some more, it'll be money well spent.

More likely is some kind of DNS issue. Group Policy settings are pulled from:

\\domain.name.in.full\sysvol

If the client can't turn domain.name.in.full into something that Windows can connect to, you'll get this kind of problem. A couple of tests to try out:

nslookup for domain.name.in.full
If it returns an IP address, or better yet a list of IP addresses, then DNS is working correctly. If it is not, then fix that problem.

Do a dir \\domain.name.in.full\sysvol from a CMD window
If the nslookup works, but this doesn't, then Windows name-resolution is failing. Check to make sure the NetBIOS TCP Helper service is running. I had one case where this service was disabled on a computer lab image, and none of the machines in that lab got GPOs.