Are the three folders, and the files within them, in the System Folder on the Desktop, aliases?
"...com.aol.aol.plist is showing as a document, as is com.internetconfig.plist. They are not referred to as files on this computer..."
That's right. I just used the term "file", to differentiate between folders & documents.
com.apple.internetconfig.plist should have been put in the trash.
"... inability to reconnect with AOL unless we restart the computer..."
If and when, we get this sorted out, the hanging disconnect may be resolved.
Although, on occasion, I too experience it.
"...we have not restored the checks on the PPP options. Should we?..."
I don't have any of the PPP Options checked. For now, I suggest you do the same.
"...And does it matter that we no longer have the 3 com.apple....plist. files..."
The only one present on my system is com.apple.internetconfig.plist.
Don't worry about the other two.
ali b