I understand that u have discarded ur old PC if so, then just ask ur service provider to reset ur mac. If you want ur old pc as well as laptop to be connected to internet then you have 2 options.
1. enable internet connection sharing on ur old PC & connect laptop via lan card & a cable, both will be able to use internet.
2. buy a small hub to connect the comps & request reset of ur mac, now u plug cable from ur service provider in the hub & can use many comps in ur small network.
LOL.................u wont need to spell all those zer000000s.
U dont need to tell them ur mac address at all, they already have that in their database , just tell them ur username or registration no. or IP address, whatever they gave u when u took the connection.
They would simply press the reset button & then ask u to connect ur laptop that would give them the laptop mac & then onwards that would be saved in the records.........................u can then surf normally.