Have you tried removing & replacing the drives (powered off)? Might be worth a shot, especially if you feel comfortable opening it & ensuring the connectors are all clean (no dust bunnies). If you have access to enough spare drives (new or used, any capacity) this would be a good opportunity to check if the unit actually works or if it’s toast using drives where the content doesn’t matter.
You can also connect the drives individually to a computer & use an appropriate utility to read out the SMART data, just don’t let it initialize or otherwise write to any of them.
You could try loading the pack into another Drobo, but I’d hesitate unless I could find one of the same model & ideally same firmware, last thing you need is anything happening during migration with a damaged disk pack.
Personally I’d be inclined to try cloning the drives & working with the clones (or in the case of recovery software possibly with disk images), possibly with recovery software ReclaiMe Pro can deal with Drobo drives & lists imaging among the feature set, disks can be cloned using any Linux live distribution & dd from the command line. At least working with clones you know no new problems can be introduced on the old disks. UFS Explorer also claims support for recovering Drobo disk packs… Neither software is free.
The other advantage of working with cloned drives is that success or failure you’ll have enough drives to populate both a replacement and somewhere to keep a backup of it.
The last advantage of working with cloned drives, is you have the originals to send to a lab if that becomes your only option.