If what you're doing is to "remote control" a PC from the Laptop, with the PC connecting to the internet with a mobile broadband connection, this doesn't seem to make a lot of sense. Why are you not just using the PC itself, or connecting the mobile dongle to the Laptop?
Plugging a USB dongle into the Laptop won't reveal either the IP address used when previously connecting with the router, or the MAC address of any network adapters in the Laptop. In any case, while connected via the router, the MAC address that was connected to the internet would have been the router's WAN MAC address, not the MAC address of the Laptop's network adapter(s). The Laptop's IP address would have been a LAN address probably with a 192.168.x.x address. That isn't an internet address and would be no different from that used by millions of other computers in Local Area Networks.
Your Laptop itself was never "visible" when connected via a router. What was visible was the router and the IP address allocated to it by the ISP.