If you are saying you have two users (different logon accounts) using the same computer at different times and one should have access and one not, then:
Cheap Simple Hack Method:
Logon the restricted account and set a dummy value such as 127.0.0.1 in the Internet Explorer > Tools > Internet Options > Connections Tab > LAN Settings Button > Proxy Server options. Drawbacks are a) only works for web traffic, b) user can change setting, c) browser dependent.
Less Cheap and Simple Method:
Use group policy.
Possibly Real Money and Not Trivial Method:
An account supporting software proxy server like
Microsoft ISA or perhaps
squid? Real Money and Complicated Method:
Install a hardware filtering gateway device such as
Barracuda Networks or
Netsweeper.
If you are saying one computer should have access and another not:
Cheap Simple Hack Method:
Remove default gateway address in network adapter internet protocol properties for the restricted computer.
Less Cheap and Simple Method:
Configure gateway router to block specific outbound traffic from restricted computer.
"Internet" access encompasses alot of things, hack methods may have undesired effects or impair other functionality.