Your connection does indeed have a port, but it isn't quite what you are expecting I'm sure and it is not something that you are going to get out of your ISP. An ADSL connection is established between a modem and a DSLAM. The modem syncs up with a port on the the DSLAM. This is typically indicated in a CO by Floor, Relay Rack Row, Relay Rack Number, Shelf, Slot, Port. This will look something like RR01.102.11.02.06.04. This however is not your circuit ID. Your circuit ID is another portion of the connection, it is typically what identifies your circuit between the MDF and the NID. This number varies greatly from ISP to ISP (and there will be more than one if you are going through a CLEC and not an ILEC as each will have their own system).
The topography of an ADSL connection is long and complex, but mostly it is a single pair that follows from the ATM all the way to your house through a series of cross-connects where it eventually hits your modem. The DSLAM syncs with the modem, the ATM provides layer 2 and at some point hits the ISP edge router which controls the IP range and routing for that region.
Your IP is handed out by the edge router - it is assigned to your circuit based on the rules your ISP has set up (DHCP, static, etc). With a bridged modem, your MAC is typically arped by the edge router, but this isn't necessarily what determines your IP - this varies greatly from ISP to ISP.
DSLAM - Digital Subscriber Line Access Multiplexer - these maintain sync and control circuit speed and perform a number of other functions necessary for DSL to work
CO - Central Office - centralized point for a city or city region where communications are connected - all COs are interconnected in various patterns, dependent on location/ILEC)
MDF - Main Distribution Frame - this is where blocks from equipment in the CO and houses from the street meet and are cross-connected between - all the services in a CO eventually hit here
NID - this is the demarcation point between the ILEC and your home wiring
CLEC - Competitive Local Exchange Carrier - not the phone company, like Covad, XO, Sprint, etc
ILEC - Incumbent Local Exchange Carrier - typically the phone company, like AT&T, Verizon, Qwest/Century-Link, etc
ATM - Asynchronous Transfer Mode Switch - these are the muscle behind the Internet