It may be too much for your power supply too.. those dell's don't come with anything great in that department.
That might be the culprit. The original PSU is (according the documentation I found) 300W. According to the
Extreme Power Supply Calculator it should be enough even with a 30% capacitor aging factor, but since the 8400GS doesn't have an external power input, it might just be possible that the amperage through the PCI-e slot isn't quite sufficient. After all, the Dell has originally been shipped with an integrated video card. It is also possible that your PSU has already blown a couple of caps. WARNING: If you don't know the risks,
don't open the PSU! There might be lethal currents left even when unplugged. Instead try with another PSU. No need to unscrew the original, just change all plugs, boot and try to install drivers. If that works, you'd need to replace the Dell's PSU.