well the easiest way to tackle this is to test the pieces separately
First less lighten the load on your power supply in the system, I know the 700w can pretty much power anything in your system right now. But maybe your power supply is defective, and it doesn't output the proper voltage. Anyway remove the non essentails... so TV card, Optical Drive and sound card should be out. If your system turns on now, plug in 1 device at a time until it doesn't. Then switch the order you put them in. This way you can tell if one of the device is the cause or if your power supply is just not working as inteneded.
Or you can try plugging in a different power supply and see if your board goes up. If it doesn't then your board is acting up. i'm just estimating here but you can probably safely power your system up with a 500w powersupply you might want to remove the tv tuner, sound card and optical drive.
After you find out which hardware is malfunctioning.. it is just a simple matter of either replacing the pieces yourself or if warranty is still good, give alienware a call.