Intermittent loss of internet

At some apparently random intervals, my internet service simply stops working.  My desktop PC, connected with an Ethernet cable, cannot connect to anything on the internet, even though the network icon’s hover script says “Internet service,” and after some random time interval it starts working again.  On my phone, I’ll get a message saying there’s no connection and giving me a choice between “Use cellular data” and “Keep trying WiFi.”  That also starts working after a while.  I have cold-booted the modem multiple times, leaving the power plug unplugged for at least two minutes each time.

Sounds like I might need a new modem?