Using CS1, Windows XP Pro.
So far as I've searched, I can find references to errors containing "can't open the illustration", but they always contain further information.
My error says only that: "Can't open the illustration." Then it proceeds to open whichever file, but it's always blank.
This is happening for most files, but not all; and it happens for .eps as well as .ai.
Furthermore, I don't believe it's file related (i.e. a corrupted file), because I can open all the files I try on another copy of Illustrator on our network.
I've tried restarting the computer.
What else might I try, short of reinstalling? Just simply reinstall?
Apparently, thanks to suggestions solicited in other locations, the resolution turned out to be renaming the documents and settings/[username]/Application Date/Adobe/Adobe Illustrator CS Settings folder, so that Illustrator would recreate the folder upon opening (similar to the common InDesign fix which I had been looking for an equivalent). Specifically, after testing, it was the AIPrefs file in that folder that caused the problems.
Now AI can save, open files, whatever.
And there you have it.
Great job, thanks for posting back to the forum with your answer. If you mark your question answered you will help others who may have the same problem.