First of all... the tech that came to your house is a retard
Azz is right on, the MAC address is a unique hard coded address, that every networking component is imprinted with. you literally can't have the same one for your PC and router. I would have seriously said "what are you a retard?" if he said that to me.
I don't know how your setup, but first thing i'd try is pull the plug on both the modem and router, plug the modem in first, let it cycle through its boot process, then power up the router.
You shouldn't have to do anything special, the router should pick up your external IP address automatically.
I'm assuming your PC is directly connected to the machine, so there should be no interference, (it will work wireless as well) pull up a web browser and type 192.168.1.1 as the address. (different routers have different IPs they assign as their gateway, if that doesn't work try 192.168.0.1, if that doesn't work, open a command window and check what your default gateway is with ipconfig)
anyway, if you get to the correct page, it should prompt you for your router's admin password, and it should work even if it doesn't have an external IP address. if you can't pull up your router's web interface... chances are your router is messed, and likely the cause of your issues.
oh jeeze..
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and that they cannot do anything on their end to clear it from their router database, and that we'd just have to wait 2-3 weeks for that figure to be purged automatically.
you're not using Telus are you? god i hate their system. if you are, you call them, and tell them you need help to register your router with their shitty system. they can either clear it, and do it for you, or talk you through it. its been a while since i've had to do that for a client, so don't remember the process. having to wait 3 weeks for it to go automatically is BS.
post more info if none of what Azz and I have suggested helps, we'll do what we can to get you going, i'm sure.