So do you mean there's a button on the base station, that press to make the phone ring ?
If so you could try taking it apart and clean the button. There could be some bad voltage/noise on the button too.
Then there's way worse problems, like something going wrong inside some micro-controller or similar chip.
I haven't taken a cordless phone apart before, but I bet they are a nightmare of micro parts, and micro soldering. And IC's with phonebook sized manuals.