This symptom indicates a hardware failure in the base station, which is a bad relay/interface on the line 1 connection. We most often see this type of damage to the base unit as the result of a power surge, either through the phone or power lines, but it can be age related failure as well.
The one thing you may attempt yourself is to fully reset the system:
1) unplug both power and phone lines from the main base.
2) remove batteries from all handsets
3) wait at least 15 minutes, then restore all
4) place a handset on the main base for a minute, as if to charge
5) check for functionality.
If the problem persists after this, it tends to confirm a hardware failure which would require repairs to correct, though repairs for these units are not feasible as it will exceed the value of the system. Your best bet in that case is to buy a new unit with a base and a single handset (you can't buy just a base): http://amzn.to/2dV7ljJ
you can then pair your existing handsets to the new base and end up with a larger system. I can guide you through that process if you go this route.
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