I am running on Vista Home version.

I just got this NEW laptop and I can't seem to share my internet connection with my xbox 360.

I have wireless internet on the laptop and an ethernet cable running from my laptop to the xbox.

I got the connection to share, but it won't identify the connection and says that it is "Local Only".

When troubleshooting on xbox live, it says that there is a problem with the IP.

I'm kind of lost on what to do now, but any help would be appreciated.

Thanks!
Try bridging the two interfaces instead.
I gave it a shot, and it signed me in and everything.

It made my laptop GO crazy though. It wouldn't identify my wireless NETWORK anymore and SAID that there was a IP conflict.

It took me about a half hour to get BACK online.Hmm sounds strange, it should work.
http://bimmergeek.blogspot.com/2006/05/configuring-network-bridge-for-xbox.html
It is the preferred method if you do have to go through a computer. You will never be able to get a fully connectible status if you use ICS.

Do you have any firewalls installed?The only firewalls I have are the ones that come standard with Vista.

It keeps saying something about an IP address conflict.Have you configured a static IP anywhere?I'm not sure.

On purpose? NoCheck your network interfaces is set to get an IP automatically and make sure the Xbox is as well.