Unplug the firewire cable and turn the drive on. The blue light should be lit, and the drive should be spinning. If the drive is not lit and the drive is not spinning, check all the connections in the power chain from the drive to the wall outlet. There is a green LED on the power adapter that should be glowing steadily. You may also want to try a different power outlet.
Once you get the drive spinning and the blue LED is lit, then you can plug it into the computer. The drive should then show on the desktop.
If the light does not come on check to see if the drive shows up in the Profiler or Disk Utility.
If it isn't showing up in either location then you will want to try different firewire ports. This is to see if any ports allow it to mount. This is to help determine if any of the ports either on the enclosure on the system your using it with may be bad.
If your enclosure also has a USB port you can try to see if it will mount via USB. This is another way to check to see if one or more firewire ports are the problem.
If you have another known working firewire cable try using that. While a cable is rarely the cause they can occasionally stop working properly.
If you have access to another computer see if it will mount on it. If it mounts and works fine on another system then it is something with the original machine you are trying to use it with.