In addition to harrymc's answer, which provides a nice way to block all network traffic, here is an easy method to keep access to your LAN (e.g. printers, NAS etc.), but to block internet access:
route delete 0.0.0.0 removes the default route from the routing table. That is, the PC still knows how to communicate with the subnet your Ethernet adapter is part of, but it doesn't know where to send packets whose destination is outside that subnet. To get connected again, just do route add 0.0.0.0 mask 0.0.0.0 aaa.bbb.ccc.ddd, where aaa.bbb.ccc.ddd is the IP address of your gateway (router).
Your password requirement is satisfied by the fact that administrative permissions are necessary to execute the route command. You can put the two commands shown above into two different batch files and create shortcuts to them on your desktop, for example. Then edit the properties of the shortcuts, hit the "Advanced ..." button and check "Run as Administrator". Each time you execute the shortcuts, Windows' UAC will pop up (unless you have disabled it or you are already Administrator) and ask for the administrator password (unless you are a member of the Administrators group).
However, please note the following:
This may or may not work well for you, depending on whether or not that PC is configured via DHCP (using DHCP, a router can announce itself as gateway, which could override the settings you have made). I would recommend giving that PC a static IP address or use harrymc's solution.
I can't test at the moment, but I suspect that the default route gets set again when you reboot the PC, at least if it is configured via DHCP, so your requirement "blocked after reboot" is not satisfied in the first place. You can circumvent this by having Windows execute your "disable-script" upon startup, for example via the task scheduler (but there are also other mechanisms). So harrymc's solution again might be easier.
I am solely proposing this because -as explained above- it is less radical and blocks access only to the internet, but not to your local subnet.
As a final word, there are other ideas. For example, remove the DNS server from the network configuration (once again, access to your local subnet, no access to internet, may be circumvented by DHCP), or have the firewall block traffic to the internet, but not to your local subnet (the firewall solution definitely survives reboots and can't be circumvented by DHCP).
The basic idea is always the same: All commands needed to implement that ideas require administrative permissions and can be used in CMD or Powershell scripts. So it is easy to let Windows handle the password part (via UAC).