Ok, I found the problem. This is very common for newbies, and it happened to me when I was first learning too. I would be working on a file, and just be clicking away. Drawing things, deleting them, trying different colors and gradients, and experimenting with filters and extensions, and everything I could find. Kid in a candy store, you know!
But as it turns out, Inkscape keeps parts of almost everything that you've done in the file, even if you might have deleted it. I don't really understand why it works like that, but it does.
So go to File menu > Clean Up Document. Well first, deselect everything. Then keep your eye on the status bar. Click Clean Up Doc. After a moment or 2, the status bar will report that it deleted 8800-something defs. (If you don't deselect everything first, you won't see the report for how many defs were deleted, in the status bar.)
Actually I feel a little silly. I should have thought of that right away. I guess you showed us the image of a couple of little paths, and it never occurred to me you might have racked up so many defs. Or maybe I'm just distracted by life offline right now....who knows.
Anyway, after you get rid of the unused defs, you'l be clicking away again
Edit
Just reviewing your original and earlier messages, and realize you showed us some different images earlier. So you might need to do this with some other files too.
There's no way to know how many defs are piling up, except after you delete them, Inkscape tells you how many. I guess it might help if there were a clue somewhere...?? Feature request??