Well, I haven't done much of anything yet except commiserate with you, but I'm willing to try. Some of the information you just provided helps us get started.
In reply to:
Your description of it as "common" makes me curious as to why I couldn't find help on the Joomla message boards.
It is not particularly surprising that the Joomla! boards don't have much about that error, as it is not particularly a Joomla! error as much as it is a PHP error, and there are several potential cause for it. We can come back to that later, after we do a little more research to help narrow down where to look. 
In reply to:
I'm not sure which logs you are describing. I understand the word "shell," but I'm not familiar with using it to solve this type of problem.
The first place to start (since you can see no obvious changes in the dates/name of your files) is to review your error logs to see where the problem started surfacing. These are located in the /home/yourusername/logs/yourdomainname/http directory (which is *above* you domainname.tld directory), which you can reach via ssh in the shell or via ftp or sftp. Lof for and download/view your error logs for around the time(s) the problem was first encountered to see what apache logged as the cause of the error.
In reply to:
I couldn't get anything to load. So, I FTP'd and checked files. No date stamps or permissions looked amiss. I manually edited Joomla's config file to set the site to "off-line" in order to provide an apology to site visitors, but that did not work -- I still got the error.
I understand, but there are a few other things you can check:
1) manually inspect the contents of your index.php file and the index.php file for your chosen template, and look for any added "spammish" links - depending upon when this all happened your account may have been compromised (though this is not likely, you should check).
2) Since all you data is in the database, you *might* be able to "resurrect" you Joomla! installation from the .snapshot automagic backup directories if you can find a snapshot that worked *before* the error manifested itself.
3) It would also help me if you can get any more complete error message than the one you posted in you roriginal thread ("Parse error: syntax error, unexpected T_LNUMBER in ... index.php at line 88"); was there any data omitted where the ellipses are shown? (I'm looking for *which* index.php the error was found in (joomla! has more than one, and I need more of the path than was provided).
Let's not worry just yet about what Norton AV may have reported (God, I *Hate* that program!), let's get to the bottom of your error condition first. 
--rlparker