... bought a GEForce 9800GT and a new power supply ... exact same problem.
When this happened to me, it turned out I'd blown my motherboard. Hopefully for you it's not that.
The monitors ... both flashed like they went into power-saving mode ...
FYI, this means no video signal. For troubleshooting, I preferred the old days when the monitor lit up with no graphics. This black power-saving screen fools me sometimes!
The troubleshooting checklist in evongugg's link is really good, you should follow that. Skip down to the section where it says assemble the system with just the CPU and HSF (Heat Sink Fan). You can do that by yanking your video card and disconnecting your drives.
However, check this out first, if it's relevant it will save you a ton of trouble.
... 305 watt Power Supply from my Dell E520 ...
A number of Dell systems have the power supply connector leads switched; for these motherboards you need a "Dell-compatible" power supply -- a standard power supply won't work and might even screw up the board. I think the "Dell Dimension E520" is one of these; I'm not sure if that's the same as the "E520" you have. Go to this PC Power and Cooling link and use their replacement power supply selector -- put in your system model and if the resulting power supply choices all say "Dell-compatible", then it may mean 1) your power supply blew and that was your problem originally; and 2) your current problem is because you have a standard power supply which isn't compatible with that motherboard. http://www.pcpower.com/products/power_supplies/selector...
Let's hope anyway because it's a lot easier to switch out a PSU than a motherboard.