Windows 1.03 (and other tools) installed on the AT&T 6300.
Geek level Fixing the AT&T 6300 / Olivetti M24 --- tech. bringing a video-troubled 6300 back to life, using spare parts.
Olivetti M24 as a Linux serial terminal
There is a lot of info online, that may help you figure out a path to gaining access to the old hard drive.
If fiddling with connectors of the hard drive mechanism, such that you are attempting to eventually mate the pins to some other input connection on a machine with ATA/IDE connectors (or perhaps a Parallel connector) ... is too much effort, I'd try to get your existing 6300 or a substitute going - running with Linux, and thus gain access to the data on your old hard drive.
Old book stores often have a lot of old Linux version instruction books/guides, that include an old floppy disc with Linux on that disc. You may have some luck, there, finding a copy of Linux that will run as the OS for your old AT&T 6300.
Gaining access to old drives via Linux - 001.
Gaining access to old drives via Linux / also via Knoppix - 002.
I should have mentioned Knoppix earlier. It's a popular Linux-based startup disc system for managing PC troubles and recovering data.