This is a post that might help anyone in the future that has a MyBook enclosure that won’t turn any longer. Although the issue could be with any of the electronic components inside (on the enclosure board itself I mean, since the hard drive not working should not cause the enclosure to not power on, *for the most part*), this is how I fixed mine with help from one of the forum members here:
Issue started one day after using the enclosure twice at the most, the power connector was not incorrectly switched with a laptop one or anything like that. The unit turned on when pressing the power button, then 30 seconds later it just shut off without any indication. Three years later I went back to try to fix it (this was a 320GB MyBook enclosure with the main board inside saying: WESTERN DIGITAL. GALAXY CONTROLLER_._ 1U PATA).
The issue was a 3.3V regulator that had failed. The regulator has three legs, one input, one output and ground. The input voltage measured at the input leg (by using a multimeter with the positive probe at the input leg and the negative probe on one of the screwholes that seemed to be tied into the ground system) was 5V. The output was ~0.82V instead of the 3.3V that it should output so that an IC that controlled the turning on of the enclosure would function properly.
Once I replaced this voltage regulator, it turned right on and I was able to measure voltage at the PATA power connectors whereas before there was none since there is another IC switch that is controlled by the IC that was not receiving the needed 3.3V.
I want to thank the forum member that helped me as he explained in some detail what components may be malfunctioning and what to look for. He will remain nameless as of now, until I get an ok from him since he probably gets enough people bugging him for stuff. =)
Hope this helps anyone in the future, that wants to get their enclosure back up and running.