It could be the port that it's using or you don't have one setup.
If your router has UPnP turned on and the Slingbox can control it then it probably used port 5201. You could setup your router to give the Slingbox350 a static IP address and then manually setup a port forward address like your classic used. Probably 5001.
Then hard reset the Slingbox and rerun setup It should then use TCP portforwarding and the post # you set it to. That should set it to the same settings your Classic used and may then work in your office.
I can try that.
I'm still trying to figure out how it is working now at all since I looked at my router and there isn't any port forwarding set up to the 350 (I see one for the classic).
If you log onto the Slingbox website, I notice port 5201 mentioned but can't see it anywhere in my router settings.
If it is a port forwarding issue, how did Slingbox tech support connect to mine using a browser?