[U2Lynne]

Is that plain ole BitTorrent that you are running, Heather? Mine looks different than yours in the preferences pane you show.

For me, I've got my ports forwarded through the firewall (althought sometimes I don't have that on). I have the same ports listed in the bittorrent client (mine just asks for one port, same with in Azureus though I use the next number up) and I have them also forwarded through the router.

If your work has no firewall, then you should be set. Or, do you have any sort of anti-virus protection on your Mac? That's the only other thing I can think of that would cause these problems.