First, the drive obviously didn't have a standard PC partition table.
# fdisk -l /dev/hdi
Disk /dev/hdi: 300.0 GB, 300069052416 bytes
255 heads, 63 sectors/track, 36481 cylinders
Units = cylinders of 16065 * 512 = 8225280 bytes
Disk /dev/hdi doesn't contain a valid partition table
I should note that I tried testdisk at this point too, but it didn't find anything. Next, I checked for anything recognizable at the beginning of the disk.
# dd if=/dev/hdi count=8 | strings
Broadcom NAS Version 1.1 MBR Tag
SYSTEM
8+0 records in
8+0 records out
4096 bytes (4.1 kB) copied, 0.00013262 s, 30.9 MB/s
After a little Googling for "broadcom nas", "hp media vault", and a few other things, I figured out there was a reiserfs filesystem on the thing somewhere. (Note: As pointed out in the first comment to this post, there is some great technical documentation on this thing online. Rather than follow it, I chose to cheat and do this the (relatively) easy way.) Google found me this nice document describing the on-disk structure of reiserfs. That's how I figured out that I was looking for a magic string "ReIsEr2Fs" (or "ReIsErFs" for version 1, or "ReIsEr3Fs" for version 3, according to some other search results). I used hexedit to find the offset of the magic string by doing hexedit /dev/hdi, hitting tab, hitting /, then typing in ReIsEr.
2685A020 84 03 00 00 1E 00 00 00 00 00 00 00 00 10 CC 03 06 00 01 00 52 65 49 73 ....................ReIs
2685A038 45 72 32 46 73 00 00 00 03 00 00 00 05 00 B7 08 02 00 00 00 CC A3 00 00 Er2Fs...................
In this case, the magic string was at hex location 2685A034, which means the beginning of the superblock was at 2685A000, or (decimal) 646291456 bytes. The beginning of the superblock is 64k bytes before that, so I set up a loop device there:
# losetup -o $[ 646291456 - 65536 ] /dev/loop0 /dev/hdi
# mkdir /mnt/tmp
# mount -r -t reiserfs /dev/loop0 /mnt/tmp
The files my customer needed were in /mnt/tmp/FileShare/.