That said, you're absolutely right in saying that I want to "solve problems" (that's just the best term I could come up with after months of trying to convey my meaning to many people--I have no attachment to it) for the intellectual satisfaction and joy of doing so. I really just love what I have done with writing code. It's really fulfilling and the structure of it resonates with me at a deep level.
So, your comment is very helpful. There's no end to the small problems or ideas that I have, especially within my work writing code. You may have answered this and I didn't understand, but the main thing I'm getting at with my OP is that I don't have the skill set to actually solve the problems. I know it probably sounds completely ridiculous, but I've approached many small problems and have always produced the absolute barest skeleton of the program which solves the problem I have. I then draw a blank on what I need to do next to continue solving the problem--the structure and the logic don't exist in my brain yet. That's what I really want to get from this thread, and I think there are some excellent responses that help with that, including yours.