I know a lot of people are suffering from this (as I just had), and
not finding an answer to this very annoying problem:

I myself had the misfortune to get exactly the same symptoms that many
have so well described: My net access would stop responding after
about 5 minutes of use upon a fresh reboot.

Surprisingly, I could get and send email, read news, but the Internet
Explorer / Netscape would become unable to access any websites after
about 5 minutes of browsing. Ping to all the sites was successful. In
my case, it happened on Windows 2000 SP4.

A second machine, connected to the same router, had no problems
whatsoever, so I knew it was not the router.

I tried everything that has been suggested here -- with no luck at
all. Anti-virus, trojan-removers, spyware scanners -- no luck.
Re-installed all network cards and drivers, networking protocols,
Internet Explorer itself, Windows Service packs -- no luck.

Then I started thinking (I know, I got the order all wrong... Maybe
next time).

The problems began after several uncusseful attempts to get VPN
software working on my machine. It would establish the connection, but
packets just won't go through. I started deinstalling/re-installing
various CISCO clients.

The new ones did not work, but eventually some old ones (3.6 and 4.0)
started to work. And this is where I started noticing that the network
stops responding (as far as Internet Explorer is concerned) after
about 5 minutes of use upon fresh reboot.

Anyway, Sorry, for the long introduction, here is the fix:

---------------------- SOLUTION ------------------------
Install any Cisco VPN client.

This installs a lot of network components. I cannot pinpoint which of
them is responsible, but with the VPN client installed, I can browse
the web all the time now. It no longer times out.

If this does not work, you may have to go through the steps that I
went throgh, ie. re-installing all network related stuff on your
machine.

-- Nick