You're on the right track thinking about using the debuugger but you don't need to single-step to the line where the error occurs. Just set a breakpoint on the line before with the "b" command and then "c" to continue to the next breakpoint. For example, to set a breakpoint on line 4 of trans.pl and go to it, I would do:

$ perl -d trans.pl 
Default die handler restored.

Loading DB routines from perl5db.pl version 1.07
Editor support available.

Enter h or `h h' for help, or `man perldebug' for more help.

main::(trans.pl:1):    open(DICT, "/usr/dict/words");
  DB<1> b 4
  DB<2> c
main::(trans.pl:4):    my $text = join('',<DICT>);
  DB<2>
[download]

From there you can get a stack trace, examine variables, etc.

Happy hunting,
-sam