I might be jumping the gun somewhat but could you saying that your H will bring the laptop home that it's a work computer?
If so then I'd guess that the most likely problem is the proxy server that it might be set up to use.
Before trying the other things below try this (presuming that you've got Windows XP, if it's Vista it should still be somewhat similar).
Go to the Control Panel and select Internet Options (or from Internet Explorer select Internet Options from the Tools menu.
Click the LAN Settings button.
There should be an area labelled "Proxy Server", if the "Use a Proxy Server etc. etc." option is selected then uncheck it. You shouldn't need to change the values entered in the boxes, just make sure the checkbox isn't selected.
Click OK and OK again to get out.
If the box was checked then the next time H is in the office he should go back in and select it.
It's also possible that the box is checked but you won't be able to uncheck it, IT departments often lock things like that down so users can't change them.
If it is locked there might still be ways around it...
If there is still no joy then check and compare the other options on that LAN settings page with your PC that is working.