Do you have a NAT-router between your network and the internet?

What exactly is being by-passed?  How is your network connected to the
internet?

What is the gateway set to on the network adapter TCP/IP setting?

YW.
Contrary to popular misconceptions, this Policy Editor, was Win98's answer
to security and user rights issues later touted in XP.
Where in Win98, the basic user was granted all rights [no security
administration unless policies were applied]; whereas in XP, users are
assigned policy restrictions upon creating the user account using
pre-made/included security policies. Same thing, only a different way to
setup, which made XP users think their system was SOOOO much more secure.
Nah, just made for easy installation by the uninformed and IT.

Policy Editor should be used with caution; be careful how restrictive you
get. And make sure you leave a way in for your self; make sure you create a
Master/Administrator policy as well.
Note: you'll have to block access in Control Panel to:
Networking;
Internet Options;
USERS/Passwords;
and related.

You'll also block the setup TABs in IE itself;
remove and/or restrict the html lnk ability to IE;
disallow registry editing and command prompt activity;
disable user access in and to the BIOS without a password [create an
administrators password in the BIOS/CMOS];
disable F8 and other bypass access at boot time [such as by REQUIRING
passwords and user accounts used];
installation of programs by the common user;
and other like restrictions.

Also, your firewall can be instrumental in blocking/restricting access by
IE/OE or any other browser or email client, and other NET access. As well as
the Hosts and/or LMHosts files.

It sounds overly complex, but there are or were some very helpful web pages
and manuals/docs for this activity, which made the task somewhat easier. And
once created, then you'd be running the same tried and true setups/user
policies once used in the business/commercial world, created by IT and the
roll-out departments [check for the "white papers"] with NT, prior to XP and
the specialty servers...
If fact, you'll likely find some pre-made policies for your desired
restrictions somewhere out on the NET [big hint].

Or, you can create a .reg file to handle much of this activity, but it will
not give the full benefit of policies.

Good luck. Google, Microsoft Knowledge Base, and Microsoft TechNet, are
your friends for this activity.