To whatsthatbug.com: we haven't found a solution yet, although I am definitely going to look into the Elieka's suggestions ... however, we did find a work-around. When we realized that we could still view "Add New," "Edit," and "Askimet Configuration," we tried adding a new plugin. When WP was done downloading and installing it, there was a link to "Return to Plugin Page" ... it worked! So, I copied the URL and can now access our plugins page by pasting it directly into the browser (after logging in, of course). It almost seems that there's just a broken link in the main menu.
It's an annoying work-around, but it does work for us ... maybe it will help you. Good luck!
To Elieka: we didn't intentionally change anything other than the content on our site, but it wouldn't surprise me at all if something went wrong during the last WP update. Thank you very much for the info ... we're looking into it now.