The second variant of Omnipotence/Omniscience/Omnibenevolence is the latter two: Omniscience and Omnibenevolence. This is somebody who is all-knowing and all-loving, but without power. I find this the most curious and most tragic of the three characters.
The tragedy comes from the natural story of the character. Somebody who is all-loving wants the absolute best things to happen for everybody - a noble and kind-hearted desire. If that person is also all-knowing, then they know exactly how to make it happen and what the results will be. But without the power to do so, that person is trapped.
I think of a character like this as a brilliant scientist. All the knowledge in the world will not give him the materials needed to make that reverse-doomsday machine. But that is what leads to the curiosity.
If you were all-knowing, then why couldn't you know how to obtain the power needed to do what you wanted? All I can imagine is that not everything is possible. Although we like to believe that everything can be accomplished with enough know-how (plenty of stories paint this picture), sometimes knowledge just isn't enough.
This person is endlessly frustrated, and fairly sad. They are an embodiment of "so close, yet so far."