My first piece of advice is to use tracert -d [ip/hostname]... d means don't look up the hostname of each computer on the route and tracert's for me are performed much faster that way.

Anyway, the problem sounds VERY strange. The tracert should always find the first few things to be the same - especially when you know exactly what those things are.

So it's still baffling me how this one website won't work. To test a little more you could try the following on CMD:
telnet folding.extremeoverclocking.com 80 (to see if it really connects at all)
if it connects you can type:
GET / HTTP/1.0 [return, return]
and see if it gives you the HTML.

Now, I can't access folding.extremeoverclocking.com anywhere at all. I've tried from 4 computers, 3 of which have unique WAN IPs, and nothing at all could see it. One couldn't look it up successfully but every one of them could ping it by IP address.

While I'm looking into how exactly to access the site (or how 'up' it is) or whatever... [ps: it looks like whatever host that is isn't running any servers at all; are you sure you can access it from your Internet computer right now?]

What port is the Internet computer on on the router? If it's a regular client port it may be the problem. I think you may have subnet issues with making the router .2.1. Here's what I suggest:
-keep the router's local IP at .2.1
-plug your Internet computer into the WAN port of the router (if they can't see each other try a crossover cable)
-enable the router's DHCP server and set non-Internet comp to DHCP client, or just give it a .2.100 IP address

What this will do is set up 2 layers of NAT, which is a little redundant but avoids a strange route. 192.168.0.100 -> 192.168.2.1 -> 192.168.0.1 might be weirding it. Or something. I don't know too much about subnets but one time I had someone VPN to a LAN party and his IP was on a different subnet (.1.x vs .0.x) and he couldn't connect to anyone but the computer he was directly connected to.

Anyway, this message is long enough good luck