It sounds like you have either a stuck button (caused by a dirty keypad) or just a dirty keypad.
Is the telephone in "speakerphone mode" when the light is on? i.e. can yu select a line and hear a dial tone without picking up the handset? Then it is likely that the "speaker" button is actually sticking down or that there is residue on the keypad causing a short.
If not, then there is probably residue or corrosion on the tracings leading t the LED indicator lamp.
Either way, the only easy way to stop it is to completely dissasemble the telephone and clean off the keypad itself.
I do NOT recomend doing this yourself!!!
Send it to a qualified repair facility, like ours [Linked Image from sundance-communications.com].