That's just an internal IP address, meaning when the 2 computers were networked they got special IP addresses so they can talk to each other with ease and much faster. Your external IP address would look something like 72.195.23.145 - something along those lines, not 10.0.0.x or 192.168.x.x which would mean internal/same network.
Another way you could have solved this would be to go to Start > Run and type "cmd" (w/o quotes) - the dialog opens and you would type "ipconfig /release" wait for a response, then type "ipconfig /renew" (w/o quotes) - that would resolve it too.
Crimsonite is correct in how to obtain an IP address assuming it was changed to manual entry. But that setting only changes if you change it yourself. Since you didn't know how to change it back, I'm assuming you didn't change it to begin with, and the IP was automatically assigned to both PC's. So, if his way doesnt work (the obtain automatically option was already chosen) then try my way. That should clear up the problem.
Hope all that makes sense. Kinda confusing...