Looks like the hard drive is connected to some kind of old connector on the PC (Bridgeboard) side. Hard to tell from the picture but I think this predates IDE - may be an MFM hard drive, or some other prehistoric format?
At this point unless there's something you really want to recover off that drive, I'd consider it toast. If you want to use the Amiga as an Amiga get yourself some kind of modern solid state solution (such as a CF or SD adapter), or at least a SCSI controller and hard drive.
It really depends on what you want to do with the system. That bridgeboard and your current expansion cards are pretty much only good for old DOS-based software. Maybe Windows 3.1 if you're really up for a challenge.
First thing's first though, take out that drive sled and remove the barrel battery before you do anything else. Search the forums for info about leaking batteries, but suffice to say it's not good. System seems to be in decent shape otherwise, be a shame to let it get ruined by a leaking battery.