Computer Identification

[DCopper04]

Does anyone know how online poker sites identify your computer? I'm sure they record your IP address, but what other information do they gather?

The reason I ask is because I have three computers in my home. On my main computer, I was recently blocked from accessing PartyPoker (I think it might be because I logged in on Party and Empire at the same time, stupid me.) Although I am unable to login from that computer, I am still able to login from the other two computers in my home. I have wireless internet; all three computers are hooked up to the same wireless router, and thus, all three computers have the same IP address. Since the other two computers are still able to access Party, that means the server must be blocking something other than my IP address. What could it be?