I tried to purchase the LimeWire PRO software, but my attempt was declined. The mentioned eventualities (The credit card or expiration date is invalid; The street address does not match the address of your credit card; The zip code does not match the zip code of your credit card; There are insufficient funds available on the credit card) do not match my case. I am uncertain only in regard of the State field, because I live in Romania and here do not exist different states in the country. Please help me.

There are sometimes problems with international people trying to purchase pro. See Problems getting your LimeWire Pro after payment or other pro payment issues, see "Account Activation" & follow the advice & links within

My situation is not "after payment", but "before payment", because my attempt to purchase was declined.

Yes but there's tips in that thread about who to contact to discuss this.
There's also more than one method of making payment. eg: money order (though a bit more expensive & time consuming)