|Interesting your vpn client does split tunnel vpn [internet and work at the same time]. Mine doesn't [sonicwall] though split tunnel is considered less secure.|
It does sound like your router is blocking returning authenication/sync requests. Find out what ports your work vpn is using and make sure they are open on your router.
If the vpn is working but your rdp isn't than make sure port 3389 is open on your router for rdp though that really shouldn't apply since you are doing a vpn tunnel.
Can you rdp to your workstation locally from a different work pc?