Pmd660 dislay too dim to read - Marantz PMD660 Digital Voice Recorder

Back - light problem. Check and replace damaged component/s at its back-light inverter board, or replace this board as card basis. If you wish to get some details; check the site linked here. Surf the site with patience. Pull up older posts. It will be best to replace the inverter board as card basis.
http://electronicshelponline.blogspot.com/
To some model sets; especially LED back-lighted types; the back-light inverter circuit will be part of the main power supply board [SMPS]. In such cases, the power supply board might need replacement.

You may download a copy of the manual here.

Did you ever find a solution to this problem? I have tried new AC adapter cord and it still has background noise. The only time it doesn't is with the batteries.

fuse

This implies that there is not enough current going to the device when running on battery (only back-light but no data) whereas running fine on AC means that the device board is most likely in a good operational condition.
I think maybe once a leaked worn battery which left forgotten inside battery compartment damaged the battery terminals or at least the wires connecting these terminals to the main board, i would recommend you to open and check on that.

I solved this problem be removing the batteries briefly so that I was able to start again with a clean slate.

I would suspect the battery tray connections are defective most likely due to a broken wire.

In your PC, right click

take out the pins that resemble watch pins! remove the stickey label with the
power switch,usb and 5 volt jack cut outs! If you have taken out the screws needed up to this point and you are a little bit technical this should get you into the unit.

If you don't have the skill, hire it out. Joe Taken