Okay, so I was thinking: Why would I be able send an image of several MB in size via forms, but I can't send this few KB of text? When I send images, I have to include enctype='multipart/form-data' in the form tag, so I thought maybe that has something to do with it. I popped that in my code, and it worked! Woohoo! So now the HTML form tag looks like: 
<form action='server-scripts/spellchecker.pl' method='post' enctype='m
+ultipart/form-data'>

[download]
Hopefully this helps others in the future.

Update: I've had a couple questions about the code I posted being what I'm actually using on my server. I want to assure everyone that I copy-pasted from emacs when creating this thread. The HTML page is called blank.html (it was just a test page), and the CGI script is called spellchecker.pl. The original spellchecker.pl had a ton of stuff in it, but I stripped it down to the bare minimum when I was debugging.

In reply to Re^2: Perl truncating HTML form input by sstevens
in thread Perl truncating HTML form input by sstevens

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