XPS Vista Network Problem - Unidentified Network - Access Local Only

I hope someone can help.  My son purchased a new Dell XPS system.  We have a wired ethernet in our home using a Linksys BEFSR81 V3.1 router which is supposed to be Vista compliant.  When we first hooked it up we could not get to the network or the internet.  After spending 2 hours with Dell support from India it worked for a while and then just quit again.  Occasionally through rebooting we can get it to work for awhile again and then it quits.  We get "Unidentified Network" and "Local Access Only" warnings.  We have three other Windows XP computers on the same network and they all work fine.  Searching the internet there are many suggestions and I've tried a few of them and they don't work.  I'm about ready to box up the Dell XPS computer and send it back to Dell and ask for our money back or go buy XP and install it.  If anyone has some suggestons or whom to contact I would greatly appreciate it.