Ok, so the patch made it worst. There must be more changes to the patch than I remember.
If you are TeamViewed into the remote computer, does that mean it possibly has internet access to let you download Wireshark directly to it. Or you could download on your computer then file transfer it to the remote PC through TeamViewer. Would they be ok with you installing it on the PC?
I won't have much time over the next few days to remote in because I am about to head to a job site to test out a new program. But on Friday I will be back at my office and will have the opportunity.