Are you remembering to power cycle the modem when switching the device connected to it? If so, try unplugging the modem for five minutes or so. I know that sounds extreme, but it's worthwhile to try.
Some ISPs require the MAC Address of the device connected to the modem to be registered with them. If yours does, have you registered the new router's or else cloned your computer's to the router?
Some ISPs require the MAC Address of the device connected to the modem to be registered with them. If yours does, have you registered the new router's or else cloned your computer's to the router?