Only f**king idiots classify Pink's music as "modern punk rock."
The punk spirit lives on in the independant music scene. Some of those bands play music in the classic punk style, so I'd have to say no, classic punk rock is not dead. It just has limited appeal, and unfortunately the word "punk" has been co-opted by PR companies. But this happens to all movements, it's not to say there aren't some people still with their hearts in the right place. You can't expect the media to promote these groups for you, so you have to look for yourself.
Furthermore, the supposed pinnacle (by common estimation) of classic punk rock, the Sex Pistols, were themselves a disgraceful cash-in (hence my utter loathing of John Lydon and co.)