Phone line is busy, but the cordless phone is hung
If the line is busy, there's a phone off the hook somewhere or there's a bad phone jack or line cord. If this is the only phone on the line, disconnect the AC power adapter from the base and also disconnect the battery in the handset. On both units, press a couple of buttons to drain off stored charge. After a minute or so, reconnect the battery and base power, and see if the line is free. Sometimes, especially in hot weather when lots of people using air conditioners or storms can cause power line glitches, the computer in the phone gets confused. This process resets everything and may clear up the trouble.
If you don't have another phone and the trouble continues after trying the reset, see if you can borrow another phone from someone for testing. If that fixes the trouble you need a new phone.
Your phone line itself might have a problem that is causing your phone service provider to think your line is in use. There may be water in the line or some other fault outside, or some problem on your inside wiring. (A friend had a problem after she plugged in a new phone, and it turned out one of the prongs in the jack had bent and was touching the one next to it. In another case, a phone jack that had gotten wet had corroded and was shorted.)
If you have other phones on the line, disconnect them all from their jacks. Reconnect one and see if the line is free. Then you can reconnect the others, checking each time. This will let you determine which one is causing the problem.
This kind of problem can be frustrating, but it can be solved. Good luck, and thanks for using Fixya!