Couldn't even come close to starting a car, the amp draw of a car starter is in the hundreds of amps. So 1000+ watt minimum.
You would want some kind of control circuitry coming from the power supply for the LED's it's the only really practical way of doing it, circuitry inside the supply would be able to tell when power was being drawn and switch on the LED's, but you'd need to run extra wires in the power cable for the LED's. Seems like a lot of effort for a little bit of silly eye candy. Though knowing the PC market there is a small portion of people that will pay insane amounts of money for eye candy like that.
If you don't know what you're doing then spec the project out to a company that does know what it's doing.