Software

You probably need a third party software program that will pop up a window to connect to the internet or intranet. Windows 7 Network and Sharing center is just for conguring the adapter and protocols for that desktop. I don't see any options to chose which network to connect to at any given time.

Not sure but I think using NAT(network address translation) would accomplish your described goals.

You can use the ROUTE command under virtually all versions of Windows to route traffic to specific interfaces, open a command prompt and do "route /?" for a full command list.
If both network subnets are on the same wiring scheme then you can simply add the two networks to the same interface and use routing rule to ensure WAN traffic is passed to your external gateway. If the networks have separate wiring schemes, then add a second NIC and only use a gateway address on the LAN connection needing to escape your network.

its easy if you add a network card to the motherboard. windows will automatically establish a secondary connection and you will have both internet and intranet running at the same time.

you can setup an additional network card in the machine. Set it to a Static IP address. The main thing is that on the secondary NIC card do not specify a gateway. This way the computer can reach any LAN specific devices but it will not get out to your firewall or router.

You may have some DNS trouble using this method on the Intranet side but test it out. Worst case scenario do a mod on the host file so that it resolves IP/hostnames with the machines you need it to see.

Routing rules can be setup as well on the machine or firewall/router, but that would depend on what's involved in your network

If you're working in a highly secure environment, then you may not want any computer to be concurrently attached to both the secure network and the public access network, since the computer then might become a bridge/router between the two networks.
In this kind of situations, many organizations resort to giving each employee two computers, to minimize the risk of computer malware / viruses reaching the secure network.

If your network is not secured to this level, then some of the previous answers may apply. (firewalls, routers etc.)

You might also look at VLAN, where the computer may use one physical connection, but where virtually all traffic is separated into different logical networks.