WOW that's a first.  What ISP is it so we can steer clear of them?  
 
One thing you could do, it'll be a bit of a challenge, but to my knowledge it's doable.  Since only one port is opened, I'd suggest, since your ISP is full of morons, you'll have to get your own router to plug into their modem/router.  Start out by taking your own new router and plugging it in and connecting it just to your computer.  If you can find out before you buy, you want a router you can set the IP address on the LAN/WAN for. Anyway, set its IP address to 192.160.0.2.  Then connect this router to your ISP's router, and connect your two computers to your new router.
Also, if the problem doesn't rely in the IP Address assignment, it'd be cheaper and more simple to buy a hub and use it in the place of the router.  That way you don't need to mess around with assigning its LAN IP address so it won't fight with your modem, and you can plug both of your computers into it. 
I'm not 100% certain it'll work, since I've never seen it done before and i don't know the specs on the ISP's modem.  In theory, however, it SHOULD work.  I do have to say though, I'm not to be held responsible for damages, losses, or anything else caused by you taking my advice.