I would start by buying a cheap wired phone, then go out to the connection box outside your house where the phone service is connected. If you open up the box, you will find a standard phone plug. Plug in your phone and see if it displays the symptoms you have described. If not, try your cordless, also plugging it into the junction box. This will tell you if the problem is your phone.
If the problem does not occur outside, then it is your home wiring. Replace everything between the box and your phone(s) insidet the house. Wires and plugs etc are all modular, so this is pretty easy to do.
I'm guessing this will solve your problem.
Good luck!