This is John at Dell headquarters.
The 8800 GTs is a fine card for gaming, and *should* be more than adequate for most of your 3d gaming needs. Your Dell power supply is beefier than the wattage would indicate, but won't support that card adequately. The 8800 GT requires a power supply that supports 22 amps on its +12v rails, the GTs requires a power supply that supports 26 amps on its +12v rails, and the power supply in the 8400 only supports 18 amps.
It looks like either way you go, you'll want a bigger power supply.
Here's an article you may find interesting:
Dell Customer Advocate