I've been able to use ICS in Windows 7 to share a connection through the available Ethernet port (when the Windows 7 machine was connected wirelessly for internet access). ICS is usually viewed as tricky to set up and unreliable.

You might be able to do the same provided your Ethernet port on the work computer is not being used. You may not have the required permissions to do this depending on the rights you've been given on the PC. You may also want to check with your company, since connecting any other devices not owned by the company may be viewed as a security risk.