There are some punk/hard-rock bands that have attempted playing classical pieces. For example Scatterbrain released a stunningly good version of Mozart's Sonata Number 3. It's on their album Here Comes Trouble, and it's also on an Australian single they released including a live version where the vocalist blames a guy in the crowd for stuffing up the guitarist's solo.

It's mad, it's frantic and it works.

Thanks to Segnbora-t for the suggestions and corrections.