I have two computers both with XP. Both are connected to a LAN connection through a Ethernet Switch. I would like to have internet on both computers but the problem is both wont run the net at the same time. When one PC is shut down the other one will work and vice versa. Further note I went to the Network options, then to Internet Protocol, and then to options. This has all been done manually as automatic didnt work I noticed both PCs have the same numbers typed in. Should the numbers be different if so where do I get the numbers to typ in?

You only get one ip address from your isp which is why you can't have both on. Should have bought a wireless router instead of the switch. A router can take that one ISP provided ip and nat it so you can have multiple private ip addresses ie. one for each of your pcs. Buy a wireless router. Give a person a fish, they eat for a day. Suggest they internet search and they learn a skill for a lifetime.

Is there no other way of doing this? I dont really want to buy another piece of equipment.

I also dont want a router because thats what I had before. I just want two direct connections to the DSL box.

You could use ICS (built into XP) and make one PC your internet "host" and the other the "client". Read the helpfiles on ICS (Internet Connection Sharing) included with Windows for setup instructions.