Thanks to everyone for the replies and information! I had already confirmed that opening the dictionary file wasn't the problem. I could print all of the words that the script read from WORD.LST, so I knew that part was working.

Looks like ysth and Anonymous Monk (man, that guy has a lot of writeups! ;o) ) had the right idea. It hadn't occurred to me that chomp on Cygwin would try to remove the Unix newline character, but the file had Windows newline characters. I replaced chomp with:

$newWord =~ s/[\r\n]//g;
[download]

and it works like a charm on both Cygwin and Windows.

Thanks again for everyone's help!