my $ueFH = new FileHandle; open $ueFH, "> my.tgz";
should be
open my $ueFH, "> my.tgz";
Or better yet,
open my $ueFH, ">", "my.tgz";
But that's not the problem.

On a Windows system, you want binmode($ueFH) in there. It doesn't hurt on other systems either. But that's not the problem if your Perl uses PerlIO. Perl ≥5.8 are compiled to use PerlIO by default.

The fact that 78MB got printed means the print was reached, which means LWP thought the request was completed. So either

1. LWP is ignoring an error,
2. LWP was told the download was complete when it wasn't,
3. LWP is reporting an error but you're not checking for it, or
4. The download was successful and there was an error saving the data to the file.

Check the status code of LWP's response. Check if print $ueFH or close $ueFH are returning an error. If that doesn't help, you'll probably have to look at the network traffic.