DIY : Powering a single LED with a motherboard's internal connectors
There is nothing special about a computer when it comes to leds. You can power directly off the ATX supply (Either 12V, 5V, 3.3V) or from the fan connector (12V). Just add an appropriate resistor and you are done. You need to apply the same led calculations as anything else:

$$Resistance = \frac{Source\,Voltage - LED\,Forward\,Voltage\,Drop}{Desired\,Current}$$

The Fan connectors have three pins, one for 12v, one for Ground, and one for Tach/Speed Sensing.


Since you mentioned cooling, are you talking about 1W or higher LEDs? The same still applies. You could use the fan connector for both a cooling fan, as well as the led power source.