Very old thread, but still comes up first when searching for "Tascam DP-01 Error" or "Failure". I had the dreaded system failure where the system would not get past the start up message. It was stuck on "Now Working...."
Here's the thing... the drive has been corrupted. You can remove the drive and replace it with another and you're good to go. The data on the corrupted drive could be recovered and put on a working drive if it's not too damaged,...you would have to get your techie friend or pay (likely) big bucks.
Replacing the drive is actually quite easy. You need an IDE DRIVE. These are the old 3.5" PATA (not SATA) interface drives with the 40 pin connector. You MUST set the jumper on the drive to "master". I bought 3 different drives, a 40Gb, a 160Gb, and a 320Gb. They ALL work in the DP-01.
Just unplug the unit, turn it over on its face, placing it on a cushioned surface. Remove the screws and take the back cover off. The drive should be obvious to find. Unplug the 4 pin (smaller) power cable, and the 40 pin (larger) data cable. The drive is held in place with brackets that have rubber mounts. It's easiest to unscrew the mounting screws on the brackets and lift the whole thing out, then take the brackets off and attach them to the new drive. Check the label on the new drive to see how the jumper should be configured for "master". Install this new drive, reattach the cables, just use a couple of the screws to attach the back plate until you have tested it, and turn the unit over.
Plug it in, and turn the power switch on. You should hear the drive spinning up and see the DP-01 start creating files. IF you see "HDD not found" then either your new drive is crap or its not set to "master".
Voila, you have your rig back!