We really need more information about your "old" modem in order to understand why the Time Capsule is not happy with the "new" modem......which is actually a modem/router or gateway type of device. By this, we mean that the Arris TG 1672G is both a modem and a wireless router in one package. There are multiple LAN <--> Ethernet ports on the back of the Arris TG 1672G.
Was your previous "modem" also a modem/router or gateway device with multiple Ethernet ports on the back the device.....or was it a simple modem....with only one Ethernet port on the back of the device? If you still have the old modem, or know the make and model number, that would be really helpful.
How can this TC be hooked up to this modem so I can use it to back up my mac mini and laptop?
Check to make sure that the Ethernet cable connects from one of the four Ethernet LAN <--> port on the Arris modem/router to the WAN "O" port on the Time Capsule. Some of the network settings on the Time Capsule may need to be changed to allow it to work correctly with the new modem/router. We will know more about this when we know more about your old "modem".
Sometimes, it is necessary to reset the Time Capsule back to factory default settings and then set it up again to work with a new "modem". We will try to avoid that if possible, but need to mention that this might be a possibility if some shortcuts that we try will not work correctly. With a new "modem", there are never any guarantees that what worked before will work the same way again.
Can the wireless signal from the Arris modem and the time capsule be in use at the same time?
Yes in most cases, although if the new modem/router and Time Capsule are located in close proximity to each other, there is a possibility of wireless interference effects between the devices. Keep the Time Capsule separated by 3-4 feet....or 1 meter...or more, if you can.
