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There may be a defective handset in the set.
Try removing the battery from one handset (with the power Off to the base station.)
Then power On the base station, and see if the problem has gone away. If it has, the handset with the battery removed is defective / at fault.
If the problem persists, then put the battery back in that handset, power Off the base station, and then remove the battery from the other handset. Power On the base station again, see if the problem has gone away - if it has not, let me know, and if it has, that's the defective handset - the one w/the battery removed.
What type of phone line service do you have?
- if a digital phone service, with a network box providing the phone line, that the phone line plugs into, then you should examine that box, and turn it Off for 10 minutes, and then see how it works after that (and if it doesn't restore operation, tell me the maker and model # ***** the phone box, and what its indicators say.)
Also if digital phone service, is there a router box also, for the internet service? if so, see if turning that Off for 10 minutes will cure the problem. (And let me know what maker/model the router box is.)
Let me know how it goes, what you find out, etc. We'll get to a solution of one sort or another with a little persistence. I will advise you further as needed.