Sounds like a corrupted system translation. If the lines are assigned to keys on extension 11 (#301) and there is no indication the lines exist when the set is programmed, it's a corrupt translation.
I've seen similar problems on several systems programmed without defaulting the system first (#989CLEAR). Most common is phantom ringing, just as you describe. The only way to verify the system was properly defaulted is on an ACS by the diagnostics program built into the remote programming suite. The very first event listed should be a frigid start - system default.
To test it (takes ~5 minutes): backup the system using #124, frigid start using #989CLEAR, then see if you can properly program 11 after it restarts in stupid mode. When testing is done, restore using #125 and retest when it comes back up and I'll bet the corruption returns. The corruption in data will be saved in any backup, so there's no way to shed it.
The only cure is to reprogram the system after defaulting it. I've seen companies trash 3 processors before I came along to default and reprogram. A lot of work, but the only way to cure it. A good tech can reprogram a medium sized system with voicemail in 3 hours (including prep work).
