Unless you are using a static IP, what you have was assigned to you after your PC connected to a DHCP server. In which case you're already working fine.
If you are not able to connect to your DSL router, its possible you have an old IP assigned from a different source (old ISP perhaps?) and your new router doesn't know about it. Try typing this (things within paren's are just comments)
ipconfig /release (there is a space between ipconfig and /)
ipconfig /renew (the first command removes your old IP, this second one polls for a new one)
And here's an interesting factoid. When told to ping your own IP, which IP are they talking about?
You actually have 2 IP's, although most hackers are only aware of one.
IP #1, the one you'll find by typing ipconfig at a command prompt is probably what you're trying to ping. To do that you have to go out to a device, and have it route back to your machine. It's possible that PING has been disabled at that device. Unless it's your local router, not much you can do about it.
IP #2... 127.0.0.1 , it's an internal IP between your PC and your NIC. Try pinging that, it'll show you if your PC is at least talking to your NIC.
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