Usually a protection circuit would kick in and the machine would simply shut itself off.
Of the "fried" motherboards that I've recently been repairing, the reverse-polarity protection components are sacrificing themselves to save the rest of the board. Thankfully, these components are easy to source, whereas the Maxim voltage regulator chip (which is what they're protecting) is a little more expensive and tougher to find replacement parts.
My guess is the blinking-lights are part of a protection/diagnostic feature. Maybe you need to hook up a meter to your power supply connector and check that you're getting a consistent (clean) 20 Volts at 9 or 11 amps from the brick.
If that's good, try taking a peek at the motherboard near the CPU by removing the CPU heatsink. If any chips around there have a small "charred" dot anywhere on the surface, your board will need repair. All of the chips should have a shiny, polished appearance.
Other than that, I can't think of any reason why the machine would shut itself down. I'm assuming you've properly installed the heatsinks with thermal paste, and have all the fans hooked up...