>Can anyone identify the programs I need
The top five files appear to be PageMaker (3.0?) documents. An appropriate PageMaker program version would normally be needed. If you are using a later version on a more modern computer, do check whether older version documents can be opened.
If necessary, you should not have a problem transferring files to and from another computer on 1.44 MB Mac-formatted HD diskettes. Any Macintosh introduced after the LC until 1997 would have a built-in floppy drive. Later models could use an external USB floppy drive. Mac-formatted 1.44 MB floppy disks can also be read by a Windows PC, but only if a Mac-disk utility such as TransMac or MacDrive is installed. There are other transfer methods as well.
Generally speaking, it is often possible to open files, and see at least portions of the contained text, by using a text editor (http://archive.info-mac.org/_Text_Processing/ or http://umich.edu/~archive/mac/util/text/ could perhaps show something of interest).
>My own Macintosh was no longer functioning, so I purchased another one (it's running 6.0.7)
Do you still have the old machine? If so, what was wrong? Does it have the hard disk drive?