I'm having internet connection problems?

I have a normal desktop PC and an HP Compaq laptop. I'm having trouble getting my laptop connected to the internet. My old laptop was a Dell Mini and it connected to the internet as soon as I turned it on and logged in. This laptop,however,doesn't make things that easy. I hit connect to connect to my network, but it says it is not able to. My desktop PC loses internet connection as soon as I turn my laptop on. With my old laptop, both computers had internet connectivity at the same time. I have a feeling I don't have the settings right that will make both computers have internet access. It's really gets on my nerves, because every time I want to use my laptop, I'm running back and forth to both computers trying to get them connected. Is there any possible way that I won't have to go through all of that trouble just to have internet on my laptop? I use a Cisco Linksys router.It is one that uses a cord, it's not wireless. I also have a broadband modem for my desktop computer if that helps. Any simple step-by-step instructions are greatly appreciated!