Not the first or the last time crap like this happens. TM won't fix their network level problems unless they happen to work on a major change and they'll keep sending technicians to you until you close the report and go away. Be prepared to wait it out (years) for them to accidentally fix it.

mztang52 has the right idea but avoid using shared VPN services which are more suitable for anonymized browsing. If someone on it gets handed an IP ban, your accounts might end up as collateral damage. (Been there done that.) Ideally, get the smallest VPS money can buy (try Amazon EC2's free tier) located close to or inbetween hops to the game server and set up a VPN. Use the PPTP (install pptpd) protocol for lowest latency, overhead and hassle since all you need for it to do is simply push packets.

There's a possibility the problem lies with the game. Game companies don't openly admit to IP range blocks (or more likely have zero knowledge of what the sysadmins were doing), but they do it all the time and it's pretty telling when it's just the login server ignoring packets like a certain Sega online game.

An alternative is to connect just to the login server with your wifi connection. It worked with that Sega game mentioned above and it might do the trick for you: