Jhieminga's suggestion of putting the HDD into an external caddy that will convert the IDE / PATA interface to USB so that you can read the data and save it elsewhere is likely to be the simplest way forward. The HDD will be formatted as FAT16, so there shouldn't be any problem with security / file permissions, unlike NTFS.
I assume that the old PC still has a floppy disk drive - do you still have a the appropriate floppy disks, and are they still readable? That system is DOS 5 / 6.X under the hood, and it's pretty easy to boot from a floppy system disk and recreate the boot files - io.sys, MSDOS.sys, autoexec.bat and config.sys, although the first 2 have to be restored using the sys command to make the disk bootable again, as they can't simply be copied over like the second 2. If you are tempted to repair the HDD, ensure that you have copied over all the data BEFORE doing anything else! Here's a helpful article on the DOS / Win 3.x boot process:
https://jdebp.uk/FGA/dos-windows-boot-process.html
Wow, blast from the past there! More than a 1/4 of a century since I had to do anything like that.