Hi hmargaryan,
Try to disconnect all the station ports & test an incoming call. If this checks okay, plug the station ports in one at a time. If it's a big system, do one card at a time. Call in & test with each port / card. This will help you isolate the fault.
One idea, check for any modems on a station port set to auto answer. Look for this before pulling all the station ports. Disconnect all modems to be sure.
A resistance across a station port that rings on an inbound call will "answer", then drop. A crushed line cord or station cable can do this. Moisture in jacks may do the same thing.
Good luck!,
-Chris