If you're not able to connect when the router is brought into the equation, it would sort of seem like the issue is with the router. You didn't indicate what specifically you're seeing as far as error messages are concerned, but a couple things you can check:
1) can you get to cpanel over the proxy domain? ie
http://cpanel.yourdomain.com
2) does your router have any sort of port limitations configured? (even so, #1 should get past this)
3) were you able to connect to cpanel over the router previously? If so, and you can't anymore, it's possible you're dealing with a server firewall issue. I don't see this being likely though unless when the router is connected your public IP changes, which is unlikely since you're still going out through the same modem to your ISP.