There are many references to this throughout these forums. If you already have an account on one partypoker skin and want an account on another, you have to open the account on a "clean" computer, that is, one which has never had any partypoker software on it.

Then, once you have the account set up, you can run it from your current computer.

Except, you may possibly have screwed up by trying to open the new account from your current computer, and by trying to contact their support. They really don't want you opening accounts on multiple party skins, so contacting support on this was a bad idea.