It sounds like your voicemail card is unresponsive. Have you restarted the phone system? Since the VM card is within the cabinet, restarting the system also restarts the voicemail. Not knowing how old your system is, you'll want to make sure you have a good backup before a restart.
In either case, it sounds like you need a certified technician to come in and look at things. All the keys and overflow destinations can be changed, but not through the phone interface - you would need the proprietary software.