First of all, it's quite impossible that someone else (legally) has the same IP number as you. A little calculation: there are 3 digits per serie, and there are 4 series of numbers. Al the numbers go from 0-9. SO! You have 12 numbers, all from 0-9. Calculate 12E10 and you have 1.000.000.000.000 different IP-numbers. Of course, some aren't used but you still have a few billion left.
Second, it could be that the site is picking your modem or maybe your proxy server. I have that same problem with Znes, if I wanna play online. But it goes right on X-Box live.
So, I have no solution, but I'm sure that no one has the same IP as you do.
I'm just a lurker these days, I feel like an 80 year old gramps, watching his grand children play outside *sigh*