My thoughts... coming from someone who has been working with Perl for basically a decade at various companies, and have had the pleasure of working with Perl experts like Tim Bunce (author of DBI) and Randall Schwartz (author of various Perl books, including the camel book).
a) Perl was used for EVERYTHING web-related in the early 2000s, but other languages and tools have come around to supplant it.
Several commenters have already said, "oh man I had to deal with this legacy perl code and it was awful," and yeah, that's a common experience and makes them think, "Perl is a terrible legacy language, I can't wait to trash it on my Ruby mailing list tonight." The negativity propagates and then people like you wonder, "is Perl dead?"
b) Web frameworks are one of those tools where frameworks like Rails and Django have all the hype. If you want to whip up your startup idea into a minimum viable web application, the trendy choice is Rails or Django. I've used Perl web frameworks like Catalyst and I'll be the first to admit banging out your "It's like Facebook... But For Cats!" startup idea is a lot faster in Rails or Django.
c) As Steve Yegge said in one of his blog posts:
'As I've done for a great many other programming languages, I've bashed on Perl's technical weaknesses at length in the past. To my continued amazement, the Perl folks are the only ones who never get upset. They just say "Haha, yeah, boy, you're right, it sure is ugly. Heh. Yeah, so, um, anyway, I'm going to get back to work now..." It's awesome. I've gained so much respect for them. It's almost enough to make me go back to programming in Perl.'
In my experience (which of course is just as anecdotal at Steve's), this is very true. Zed Shaw writes yet another blog post blasting whatever technology crawled up his ass and died, and we just smirk and update our modules on CPAN. But while that means we're not getting caught up in the "narcissism of small differences" (to refer to an earlier commenter), it also means we're not part of the noise on the web. There will probably never be a "Perl is a Ghetto" blog post written, and while that's obviously a good thing, it can also lead to the perception that, "man, nobody's talking about Perl, nobody's even bashing Perl, is it dead?"
d) That said, in my opinion these languages don't hold a candle to Perl when it comes to back-end engineering. We love talking about startups here at HN and thus, we talk a lot about startup problems and their solutions. But if your startup actually grows into a real company, you're going to encounter problems like, "we need a system to allow our analysts to manage our SEM campaigns and reconcile our cost and revenue" or "this partner doesn't have an API so we need to spider their interface to get the daily data and import it into our data warehouse." And any company that dismisses Perl as an option for those problems just because of (a) (b) and (c) is doing their company a disservice.
TL;DR -- Perl's strengths don't match the trendy topics on communities like HN, but it still has real value for real business problems.