In System 6 and earlier, the Desktop Manager (apologies if the name is inaccurate) is not very sophisticated. When file associations are broken, you can often fix them by locating the application that you want to open a file type and duplicating it. Then delete the original version. The duplication process updates the "desktop database" which is basically a resource that acts as a lookup table.

Alternatively, plonk a copy of the desired app on the desktop and use it to open your files on demand.

Your old Mac won't map file extensions to an application unless you have a mapping INIT installed (eg a very old version of Internet Config). However it is possible that your hard disk is messed up and a clean build would make sense. If you have done a clean build, ignore the last sentence.