Time capsule does not connect to the Internet! Help!

The Apple routers have known problems with some modems.. of which you picked the second worst.. SB6141 is the most noted as problematic closely followed by SB6121.

The issue is most notable with the AC model Airports.. whether TC or AE.

Fixing the issue maybe impossible..

First off it sounds like you may not be swapping modem to client or router correctly.

When you swap from a directly connected computer to the TC you MUST power off the modem for about 15-20min.. are you doing that??

If not that is what is needed..

If you already have done that.. sorry it is simply the compatibility issue and it won't work.

Are you in IPv6 area you must set IPv6 correctly..

See http://mydeviceinfo.xfinity.com/download.php?file_id=35

I have to quote from Bob as I am not on cable.

Zoom modem.

https://discussions.apple.com/thread/7360161

https://discussions.apple.com/thread/7427491

There is nothing wrong with the SB series modems.. the issue is the apple router..

A better solution IMHO is to replace the TC as router.. you can buy a cheap router like the WR1043ND which is plenty powerful enough and only about $50 in the US.. you can use the TC still plugged into it for wireless and TM backups.

I am on Comcast and I looked up Airport before I bought a new modem - the research I had done seemed to indicate that Airport Express could not function as modem / router with cable - I went with Dlink DCM - 301