No I don't believe Dell keeps a record of the NIC MAC address. In any event it wouldn't do you any good, there no way to tell what the MAC address is just by logging into a ISP, unless they authenticate by the MAC. Which I don't think they do, it's usually done by username and password. If this laptop had a unique username and password to logon to the ISP then you could probably find out when it logged on but at to whether they could give you a phone number to go along with it that's something you're going to have to ask the ISP.

just report the case to Dell, and Dell will keep track of the service tag.

(in case the notebook is needed to be serviced in the future)