Finding router's WAN/External MAC address
If your router has an Ethernet plug (same as the "network" plug on your computer) on the external interface, with a bit of luck you can get its MAC address from traffic.
- Install Wireshark (a packet analyzer) on your computer
- Note how your computer and the modem are physically networked (you'll want to go back to this state later)
- Start Wireshark and set it to capture in promiscuous mode, on the computer's network interface (most computers only have one, anyway; you are looking for the wired interface, not WiFi)
- Connect the computer to the WAN side of the router
- You should see some traffic on the wire:
- Clicking at the packets in the upper pane, a detailed view of the packet will open in the middle pane. There, you should see MAC addresses of your computer and of the router's WAN port (see image). If the MAC address is ff:ff:ff:ff:ff:ff, ignore that and look at some other packet (as that's a "broadcast address", which is not useful for us here)
- You should only be seeing your computer's MAC address, the broadcast address, and the router's WAN MAC address here.
- Stop Wireshark
- Revert to the network setup you have noted above.
From your comment, this looks like the router you're using. I can't find an English-labeled schema and I don't speak Turkish, but if you are currently connecting to your ISP through an ethernet cable in Port E, this approach should be applicable.
Your ISP can detect it as they are directly connected to your router. They could do a broadcast from the other side and get the MAC using ARP.
A website or other internet connected host can't tell you what your WAN MAC would be: as an IP packet travels through a network it uses for each hop a different source and destination MAC address.
See for more info: http://msdn.microsoft.com/en-us/library/ms817953.aspx
So, your options are:
1) Ask your ISP, though the chances are slim to none that they will tell your MAC.
2) Ask your ISP if they want to allow your own router.