I'm assuming that the DSL modem is external?
If so, you would need 3 cards total, two cards in the HP and one for the Compaq. One for the modem and one for each system. If you are not going to use a hub, you will need a crossover cable between the two systems. This will only work if you have Win98SE or Win2K and enable Internet Connection Sharing (check the help files for how) or you buy a third party software which is sometimes best.
Another solution is to use something like a Linksys Cable/DSL router. you wouldn't need the third card and it can act a a DHCP server and firewall for about less than $180.
It's going to depend on how you want to set up your network. Will you need to expand in the future?
These were simple answers so do a lot of research.
I hope that helps you.