There are many ways in which the system could have "No Internet" and the answer really depends on what you mean.
As the accepted other answer suggests, you could simply disable the network interface. That guarantees you have no internet, but the computer also will know it has no network either.
A couple other options are
- To remove your Default Gateway (this may require setting static IP settings in the control panel, though I'm sure you could do it programmatically as well)
This way, the computer still thinks it's connected, but it won't have any network access except on the local subnet
- Remove DNS server settings, see above link.
This way, the computer has direct IP based access but to a regular user it would appear as if there was "no internet."