I guess you are using cable modem..??
You cannot change over clients without turning off the modem for a length of time that allows the ISP equipment to reset the MAC address of the device that captures the IP.
It can sometimes take, 15min off or even overnight for the modem to reset.
When it turns back on.. you must have only the TC connected to it.. the first device turned on will capture the IP.
So make sure the TC is plugged into modem.. it must be from WAN port.. (next to USB).
Power up the modem after the off time.. then after 2min power up the TC.
If your modem is not cable tell us.
If this doesn't work tell us precisely the modem make and model, and your ISP.