this is crazy...
what does ipconfig /all show when you are connected to the domain, connected to wireless (as you just described), or out of the domain
when it's not working can you still ping outside addresses (like 69.147.114.224 for yahoo.com)?
what do you get when typing nslookup at the command line?
check the group policy, is there anything useful? what about event log - anything show when you're off the domain?