Need to run XP Wizard on each re-start. Help!

Perhaps you can help with this mind-numbing problem.

I have three XP computers plus a wireless access-point feeding off a LinkSys 4-port router connected to a DSL modem.

The router is new. The reason I bought it is (I think) irrelevant. Prior to this, I used a one-port router and a 4-port switch and all worked well for a couple of years at least.

I set it the new router up per instructions. Two of the computers as well as the access point work fine. You turn on the computers, and the network is up and running. They can talk to each other and to the Internet.

The third computer doesn’t see the network on start-up. I go into the XP wizard on the third computer for establishing a network, the wizard does its thing, and within a couple of minutes all the computers are up talking to each other and to the internet. From then on, all is well.

However, each time I shut down and restart the third computer, I have to go through the wizard routine all over again.

I called LinkSys and they verified that the settings I inputted on their router were correct. Nevertheless, they graciously sent me a replacement router, I plugged it in, and same problem persists. I switched some of the Ethernet connections into the router to see if it would make a difference which computer would come up “dead”, but it doesn’t matter. It’s still the same one. I don’t think the problem is with the router. I tried a substitute Ethernet cable from the third computer to the router, but still get the same result on startup.

Any help or suggestions will be enthusiastically appreciated.