Just bought an used 8800GT pulled from a Dell, sold as is.
 
I performed the following: disabled on-board computer, installed Nvidia drivers for new card, turned off computer and disconnected power, and installed new card in PCI-e slot and power cable.
 
Then I plugged monitor to new card.  Reconnected power.  
 
First the computer shuts itself down three times before boot, then stays on after the third time.  At this point there is no screen (monitor LED still "off" with no output from card) and the computer doesn't boot - keyboard lights don't flash and no beep.  However, all fans are blowing, including the card's.
 
Switched monitor to onboard video - nothing.  Turned everything off and removed card.  Computer boots normally with onboard video.
 
Solution?

It could be a number of things, but it's hard to say without more info.
 
One it could be that your PSU is too weak.
 
Two it could be the card is bad.
 
Three (i could be wrong) but i think your supposed to install the new drivers AFTER the card is installed.  It might not matter though.

Sounds like a bad card to me

Made sure all your connections good? The 6 pin to the card? etc?

Yeah they sold you a bunk card dude.  I am going to go with the card was pulled because it was bad.
 
a few things you can check  
 
make sure you have proper power cables connected to the card.  Are you using a pcix power connector directly from the psu unit or one of those two cables  that takes two molex into a single plug for the card that comes with it?  
 
Also, another test could be try it in a different computer altogether if you have a buddy or something that has one.
 
But yeah, overall prob a bad card sold as is because well, its broke.
 
Best bet is to contact the manufactuerer, I have no idea if dell buys a certain brand xfx, evga or whatever see what they will charge to fix it if its even possible.
 

My PSU is rated at 450W.  And yeah, I have a two 4-pin molex into 6-pin adapter plugged in.
 
Think I'm going to go with "bunk card."

 
The W of your psu is not the most important part of determining if it can power your video card.  What's the most important is how many A (amps) on the 12V rail it supplies.  Check the sticker on the side of your psu, and compare it to what the manufacturer says for the video card.
 

Un-install ALL the drivers.  
Uninstall the card and start all over again.
You should not install new video card drivers until after installing and booting with the card in.  
Other than that, I dunno. Could be a lot of things.

Well what happens is when the OS loads and the previous driver package does happen to be installed still, it simply won't load the driver and the driver will remain installed until you install a different force ware version. Now there's is a little trick I like to use when I install my drivers: http://downloads.guru3d.com/download.php?det=745
Install it and run it. Select nvidia and do a complete wipe of old files AFTER you have uninstalled the driver, then reinstall the newer one.

and what motherboard is this on? 18A +12 rail for the 8800GT <--- yep that's accurate

^ Well it goes without saying that one should un-install all old drivers before trying to boot with a new video card. However, you should NOT install the new drivers first, before you install the card.

Even if the 450W psu doesn't have enough juice for it, you would still think it would boot.  I'm calling bad card, maybe boot without anything in the 6-pin power connector. It should give you an error in windows that it does not have enough power, but you should be able to boot with it.