My guess would be that the nicad batteries in the Partner have died, the customer had a power failure, and the setting for MOH reset itself to default (no MOH)
The adapter is probably OK, you just need to set it for MOH again.
Here's the Overlays:
MLS-12D
Partner 18-D
MLS-34D ftp://ftp.avaya.com/incoming/Up1cku9/tsoweb/partner_acs/prp34dol.pdf
And the actual instructions:
Programming Music/Tones on Hold
This must be programmed from extension 10.
1. Press [ Feature ] [ 0 ] [ 0 ]. The phone beeps once, and the light next to [ Spkr ] is green flutter.
2. Press left [ Intercom ] twice. The light next to left [ Intercom ] is green steady.
3. Press [ # ] [ 6 ] [ 0 ] [ 2 ]. The Message light is red steady if the current setting is Tones On Hold, red wink if it is Music On Hold, or red flash if it is Not Active.
4. Press [ 1 ] to select Tones On Hold, [ 2 ] to deactivate Music and Tones On Hold, or [ 3 ] to select Music On Hold. The Message light changes to show the new setting.
5. If you make a mistake, begin again at Step 3.
6. When you are finished, press [ # ] and a three-digit code for another option or press [ Feature ] [ 0 ] [ 0 ].