Try resetting your router to factory defaults via the reset button on the back. You may need to restore some configuration settings after you do that, but make your router configuration as simple as possible to start, so you can see if there's something that you changed somewhere along the line that's keeping your router from working with your company's VPN.
I'm assuming you are right, it has to be a router setting, if you can connect from other networks but not your own. I assume you can connect and access the web etc. from your computer if you are NOT on VPN. It's rare to encounter a networks where I can't use VPN if i can connect successfully and access the web. Can you connect and actually reach external websites if you aren't on VPN?