In my Ubuntu 9.04 installation, just a few days ago, I lost my usage of
the internet. I still had internet access. Firstly though, there was a
problem with the router, so I tried a friend's router (both Netgear
DG834) and the friend's one worked.

But in Ubuntu, I could not access any web pages or email. Skype works.

I tried using my netbook and that could access web pages okay.

So then I booted my main PC into the old installation that I kept there
of Ubuntu 8.04, which I am using now. And in this the internet works
just fine, I can access websites and download and send email.

But in Ubuntu 9.04, it seems like something is blocking my access. I do
not recall installing anything new, although something may have been
updated recently. I can see the DNS servers from Ubuntu 9.04 and it gets an IP address from the router.

What is the likely cause of the Internet being blocked for websites and
email (but not Skype)?

Suggestion -

If you happen to be using Firefox (for example)...
... and Firefox happens to be configured for "offline" ("File, Work Offline= Y") ...
... then that could certainly account for the kind of behavior you're seeing.

At least on Firefox

Just a thought .. PSM

Have you tried reinstalling webbrowser or installing another browser?