What was the reason you installed a new heat sink and CPU fan? Sounds as if that Latitude doesn't like what you did. The Latitude will check voltages for CPU cooling and will not start if they are outside normal operating perameters.
You need to calmly go through every thing involved in the changeover, including the labeling and specs for the CPU fan.
Since you obviously had the computer disassembled, perhaps you inadvertently left some component uninstalled, unplugged, or too loosely plugged.
I would go through every pin and cable, and remove then reseat everything you can reseat. By removing, then reseating, you reaffirm that the connection is the best it can be.
Also, because Latitudes become brittle as they age, use a strong magnifying glass and bright light to assure you didn't crack anything or bend a pin.
If you removed the CPU, look for bent pins there.