Connect to your slingbox at work; then click Settings next to "Watch". Under the video window, click network details. Make sure the Slingbox hasn't tried to use another port and that the IP address the port is set to is correct. My Solo wanted to use .254 all the time; my 350 likes to grab the first one open. If that's the case, you may need to ask IT to not only change the port the IP is forwarded to; but to assign a DHCP reservation to prevent the 350 from changing IPs.
Does slingbox.com need to reach into my corporate network or does the 350 reach out to slingbox.com to establish the connection? Big difference.
It's actually not slingbox.com that reaches in to the network; but it's the client. Your account contains the various internal device ID's of your Slingbox unit and the website merely "keeps track" of them. Your Slingbox will talk to slingbox.com merely to let it know if it's available and what it's status is. When you attempt to view from the software; the software itself is directed directly to the slingbox.
So, let's say your corporate public IP is 184.108.40.206 and the internal IP is 220.127.116.11. What's going to happen is the software is going to attempt to connect to 18.104.22.168 on the port the slingbox told slingbox.com it's on. The program then attempts to make a connection directly to 22.214.171.124 on the port it's told. If all works well, the firewall will route the connection on that port to 126.96.36.199.
Basically, you have to make your 350 connectable. Your firewalls have to allow the connection. If your corporate network has multiple IP's, that could probably add confusion to it, maybe not. I haven't used them in a multi-IP environment.
But, you need to be able to connect directly to the thing from the internet.
Assuming the 350 is at work and you're trying to control it from home, imagine your work has a receptionist. If the receptionist (router) doesn't know what to do with a visitor (incoming request to talk to the Slingbox) it will ignore it. You have to tell the receptionist (router) what to do with the visitor (incoming request)--your IT staff has to either:
1) Allow UPnP devices to configure the router, or
2) Manually route port 5201 (preferably both TCP and UDP) or some port above that (5202, 5203, etc.) to your Slingbox's IP address. Note this would require a static DHCP reservation for the Slingbox
The feasibility of either one of these depends on your particular office and IT staff. As the size of the organization increases, the odds of achieving either of these likely decreases unless you have significant clout in your office.