Spectrum internet service and Airport Time Machine

My internet service (Spectrum) failed, so I called Spectrum. Spectrum said it was an "Apple wireless problem," and referred me to Apple for assistance. I held with Apple for over 90 minutes but gave up at 1.5 hours' hold-time.

Spectrum said I could use my internet if I connect their modem directly to my computer (bypassing the airport extreme/time machine). Indeed, this worked. In this way, I can access the internet, but I am unable to use my Apple TV, Time Machine, or my wireless connection. Seemingly, neither Spectrum nor Apple have or plan a solution. Can anyone advise or shed light? Many thanks.

All best wishes,

Paul.