The fact both handsets are affected rules out keypad errors. Do you have an old analogue phone gathering dust anywhere you can try? Or can you borrow one if not?
If that works then check the line cord from the base station for damage or a loose connection. You can also try a factory reset of the base station as per P.67 of the manual, but you may lose your contacts.
If it's still the same with another phone then likely a line fault as @Keith_Beddoe suggests.
