Hello,
If the only thing you want to do is to weed out the blank lines, a one-liner could do the trick:

*nix version:
 perl -ni.bak -e 'print unless /^\s*$/' myFile
Win32:
 perl -ni.bak -e "print unless /^\s*$/"  myFile
[download]

In the future, you may want to check the search functionnality of perlmonks, I found all these relevant nodes about your question:

• Cannot seem to remove empty/blank lines
• How do I remove blank lines from text files?
• How do I strip blank space from the beginning/end of a string?
• and probably a bunch of others...

Cheers,
Briac

Update:
For this node to be really useful here's why your snippet doesn't work:

Your regex did indeed match an empty line, but the newline "\n" character is not matched by the regex. So your program happily replace an empty string (with a non-matched newline) with another empty string (with the newline it has not matched). Should you have chomp'd the line, everything would have run smoothly (but you'd then have to add the newline at the end of the lines you want to print)