That helps. correct any of this if its wrong.
Your router has 2 ports on the back. one of your Internet (WAN), one for you Local network (LAN).
Only one computer is plugged into the network at a time?
If all of these are correct then you can have the same IP address for each machine since only one is actually connected to the network. Sorry I was under the assumption that they where each running on the network at the same time.
Since this is a modem you might have to reboot it when you change the PC, (this is something im not 100% sure on)
Since you stated that you reset your modem in a previous post.
Connect your PC to the modem.
open your browser and type in http://192.168.2.1
You will have to supply log in username and password. (this was probably given to you with your paperwork or you configured it yourself).
This is where I'm hoping to solve your problems. I have experienced modems like this before that you have to log back into them with the information provided to you from your ISP in order for it to connect to the internet again.
After you get in if your internet does not come back up take a screen shot of the settings and we can work through getting them configured again.
I would also suggest looking to see if your modem has a bridge mode. buying a stand alone router, switching the modem from router mode to bridge mode and connecting your PC's to the router.