Then your system perl is still broken because /usr/bin/perl should be an ELF executable. I suggest you move your script out of the way and try apt-get --reinstall perl again.

My advice is to always leave the system perl alone and install your own perl for your own use in a separate directory.

Update: forgot -- on --reinstall as I usually use aptitude.

Are you sure this is necessary? Can I test if my system perl is broken? Everything seems to work fine.

I'm not sure that it's necessary to fix your Ubuntu installation but you will probably run into problems down the road if you don't. It used to be that your package manager would be broken by now but apt has been moving away from the perl dependency so you might not ever notice. At the very least, perl programs installed through the package manager will be broken.

You can check the system perl with
/usr/bin/perl -v
[download]
which should say something like
This is perl, v5.10.1 (*) built for x86_64-linux-gnu-thread-multi
[download]
You can also check to see what kind of file it is with
file /usr/bin/perl
[download]
which should say something like
/usr/bin/perl: ELF 64-bit LSB executable, x86-64, version 1 (SYSV), dy
+namically linked (uses shared libs), for GNU/Linux 2.6.18, stripped
[download]
If your system doesn't give similar responses, your system perl is broken.