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Let's try to troubleshoot this problem "long distance"! Since the problem is related primarily to incoming calls, there is only a slim chance that the problem is in your actual wiring. All signals in either direction use the same wires. However, you may have a bad connection or reversed wiring at one of your phone jacks. You can test all jacks with a telephone line tester, available at Radio Shack and many hardware stores. (If you are using multiple lines, get a multiple line tester.)
Though you can test each line with a working telephone, you will not be able to tell if you have any mis-wired jacks. Each telephone line has two wires and, though the phone may work if the wires are backwards, multiple phones on the same line may have problems.
If all the jacks are OK, you may have a problem in one of the phones. One bad phone can bring down an entire line. Test each phone individually for both incoming and outgoing calls.
There is one last consideration that should be examined. There is a limited amount of power available from the phone company to make your phones ring. In other words, if you have too many phones, none of them will ring or they will ring inconsistently.
If you call the phone company, they can give you your system's REN limit. Then, add up the REN of all your devices on the line. If they are less than the REN limit, you are OK. If you have exceeded the REN limit, your problem might be there. The solution would be to eliminate a phone or phone device.
Most phones have a REN of around 1. Computer modems, fax machines, and answering machines also have a REN value, and you should take them into account when figuring your total REN. I have an ancient US Robotics Sportster Voice Faxmodem, and it has a ringer equivalence of 0.4. My answering machine also has a REN of .4. As you can see, "non-ringing" phone devices use only a fraction of the power of ringing devices.
The REN or "ringer equivalence", by law, must be printed on the device. Most are on labels under the phone or device.