I would like to connect two LANs from one PC. The first network will be used for application software and the second for Internet and e-mail. The application network is owned by another company and the second network owned by us.
-- Ali Al-Kangooni.

First, find the IP addressing scheme used on both networks.

If the IP subnets on each network are different, one option is to install a second network card. When I tried to do something like this in the past, I occasionally ran into some routing problems with XP. You may need to do some tweaking with the routes on your computer. You might want to try putting some static routes for specific hosts or possibly the subnet you are trying to reach with the second network card that specifically point to the second network card. After doing this, check that you have a default route to handle all remaining traffic over the primary network card.

If you think you might ever want to connect more than just one computer to both networks, there is another option. By using a router with multiple network interfaces, you can have just one network card in the workstation and let the router do what it does best, handle the routing between the networks. You can setup the access control lists on the router so that only one workstation can reach the host(s) that you need to be able to connect to.

If the router option is almost but not close enough, you can either upgrade the firmware on the router so that it has firewall functionality or look at putting in some type of firewall so that you can not only control the system(s) allowed to pass through the connection but what ports are to be used between the connected systems. This option might be a little more expensive but might give both companies the desired comfort level so that you can have the desired connection but with sufficient protection that is important to all concerned.