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Since I have an IP for my PC that is known on the internet maybe I could setup a web server or VNC into my PC from the web, couldn't I?

Yes. You don't even need a static IP for that, but you do need to either control the NAT device to allow incoming connections, which I assume you can't do, or it needs to not be NATted at all, with your PC itself getting the "random" address, which is not how it seems to be set up in your case. So while it's not the static IP itself that would allow you to do that, the side effects of ordering one in your case is what would allow that.
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Bitt Faulk