Ok, Fixed it.
Zx7R was on the right path. Here’s the steps I used:
1.) Download procMon.exe from Microsoft. Run procMon, filter on the BTSNTSvc.exe
2.) Turn on your queue, make sure you’re receving the “GETTempFileName Failed” error message.
3.) Check procMon for Operation CreateFile, you can also filter on this. You should see where BizTalk is trying to write to a temp folder and is getting an ACCESS DENIED error. For me, this location was: C:\Users\BizTalk_User\AppData\Local\Temp
4.) Go to that folder, and give the MSMQ user access. Done, fixed!
-Clay