Although you have reasons to trust the battery, they have to try the AC adaptor first. 

If this does not solve the problem, it could be the motherboard.

If the new adaptor does not solve the problem, and since the machine is brand new, I would call Dell back and arrange to send it in for service right away. The sooner it gets to them, the sooner you get a working machine again. They pay for everything including the little padded box.

Thanks texasnutmeg and seventyseven for your replies.  Makes sense that they want to try the AC adapter first.  Just thought I'd ask if anyone has had a similar experience as I've lost faith in Dell support.  My company bought 4 matching 8600's in January and we've already had to replace one of them.  We have next day onsite service, but we're finding out that next day service means that Dell will send a contract repair person who may know very little about fixing the computer.  The guy they sent us didn't even have the basic tools that he needed - I had to let him borrow a screwdriver.  Guess I'll see if the new AC adapter makes a difference before worrying much more about it. 

Although you probably already got this issue resolved, The most likely cause of this problem is not the powersupply in side the laptop there is a short from the connector where the power cable goes to. That would explain why the light is on with powersupply plugged into the outlet but not the computer and as soon as you plug it into the computer it detects the short and kicks the power supply off.

Dont get discouraged with dell, things like this happen no matter what computer company you purchase, as technology becomes smaller and more advance so the do the complexity and possiblities of problems.

Thanks for your input nw15062.  The issue actually hasn't been resolved yet but hopefully it will be by tomorrow.  I got to work this morning and connected the computer to my port replicator (which includes an AC adapter).  Again, I was unable to power up the computer and, as with the AC adapter, the power light on the port replicator went out as soon as the computer was docked.  I called Dell support again and they're sending a technician tomorrow to replace the motherboard.  I'll post an update after that to let anyone that may be interested know the outcome.

any updates!!!

My computer is back up and running.  A service tech came to the office today and replaced the motherboard.  As soon as he had all of the screws back in we gave it a try and everything seemed to work fine.  I had to hurry off to a meeting, and upon getting back to my computer about an hour later it was locked up.  Neither the keyboard or the touchpad would do anything so I held down the power button until it shut down.  After that, every time I tried to boot up, the power light would come on, the caps lock light would blink for 3 or 4 seconds,  then everything would shut back off.  I called Dell support and the phone support guy had me basically remove everything - the battery, hard drive, cd-rom, ram, wireless card, and modem.  Then I added each one back one at a time, booting up successfully then shutting back down before adding the next item until everything was finally back in place.  That seems to have fixed it - I think the ram was probably just loose.  Hopefully I'm finished with that headache for a while.  Thanks to everyone who posted replies.