Pooka, me thinks there'll be no need for you to check the settings once the new router has arrived: both your pc's are on automatic settings, they will both ask the router for an IP address, and the router will assign both of 'm a unique address. No need to check, no need to change!
At Snacko: Yes, you're right.
But your idea to bypass the router would not work, as Pooka said.
The things we looked at we're the only things we could try... for now...