How about your ISP? Do they firewall at that level?

You have narrowed down every other possibility to just this one.

The only way we can prove that theory wrong is for you to either A) log your computer in via another ISP, or B) allow me access to your account to see if I can recreate the issue on my own computer.

I've talked this one over with techs at Jelsoft (the company that sells the vB software) and also with a third party that has written several add-ons for vB software. In every instance, we come down to the same common possibilities -
  1. Browser settings
  2. Security settings
  3. ISP
  4. Browser cache
  5. Firewall
  6. Anti-Spyware and/or ad blockers
In your case, we can clearly rule out nos. 1,2,4,5 & 6, leaving only your ISP as a possible suspect.

I display a logo for one of my affiliate advertisers on my own sites. If I use the computer at my work office, the logo does not display. Everything is identical about that computer and the one in my home office - same browsers with the same configurations, same local firewalls with the same configurations, etc. The only difference between the two installations is the ISP. I can examine the page source code from the office box and see the lines calling the logo, but it will not display.

If you are interested in my testing it further, I can change your account password to allow myself access to your account. Once we are finished with the testing, you can change the password back to whatever you want to use. Or you can take your box to a friend's home and log in via that ISP to perform your own testing. Barring that, we will have to simply assume the ISP is the culprit and consider the matter closed.