A change of modem needs a full reset of the Airport router. In your case a Time Capsule.
Factory reset universal
Power off the TC.. ie pull the power cord or power off at the wall.. wait 10sec.. hold in the reset button.. be gentle.. power on again still holding in reset.. and keep holding it in for another 10sec. You may need some help as it is hard to both hold in reset and apply power. It will show success by rapidly blinking the front led. Release the reset.. and wait a couple of min for the TC to reset and come back with factory settings. If the front LED doesn’t blink rapidly you missed it and simply try again. The reset is fairly fragile in these.. press it so you feel it just click and no more.. I have seen people bend the lever or even break it. I use a toothpick as tool.
N.B. None of your files on the hard disk of the TC are deleted.. this simply clears out the router settings of the TC.
Setup the TC again.
ie Start from a factory reset. No files are lost on the hard disk doing this.
Then redo the setup from any of your computers. Or iOS device with airport utility for iOS loaded.
1. Use very short names.. NOT APPLE RECOMMENDED names. No spaces and pure alphanumerics.
eg TCgen5 and TCwifi for basestation and wireless respectively.
Even better if the issue is more wireless use TC24ghz and TC5ghz with fixed channels as this also seems to help stop the nonsense. But this can be tried in the second round.
2. Use all passwords that also comply but can be a bit longer. ie 8-20 characters mixed case and numbers.. no non-alphanumerics.
3. Ensure the TC always takes the same IP address.. you will need to do this on the main router using dhcp reservation.. or a bit more complex setup using static IP in the TC. But this is important.. having IP drift all over the place makes for poor networking. If the TC is main router it will not be an issue.
In this case you will bridge the TC because the ARRIS TG1672 is a router.