How can I troubleshoot unsuccessful knife-sharpening?
Take a marker to your knife edge so you can actually see how you're removing material from your knife.

Additionally you probably need to get another cheap stone and soak it either in water or oil, depending on what the stone calls for. You want to make sure the stone is producing a paste for you, and you want to make sure your stone is flat. Getting better stones won't really help if you're using the stones incorrectly in the first place. Get a one dollar knife you don't really care about and then sharpen the knife till you develop a burr on one side of the knife. Then Do the same thing on the other side of the knife. Then you want to strop your knife on some news paper or on the edge of some cardboard. The actually motion for stropping a knife is the same as sharpening it only stropping is more forgiving than sharpening is. 

Additionally, you want make sure you're stop sharpening your knife at the right grit for what you want it to do. I typically sharpen with sandpaper so I can't really give you grit numbers because natural stones have different grits than sand paper and diamond stones. The general rule of thumb is to start on a lower grit to remove material faster and move to a higher grit to get a more refined edge, then strop to further refined edge and to clean up the blade/remove the burr. 

Generally speaking, if you're using a general purpose chef knife, you want to keep a consistent angle of around 20 degrees when you sharpen a knife. The marker you paint the edge with will help show you where you're not doing that. it will also show you where you're removing too much material from the blade and where you're not removing enough material from the blade.

A final thing you want to do is to check your blade for nicks. If your blade has nicks in the edge then you're going to have to remove material till you remove the nick in your blade. That could be the issue you're running into. orient the blades edge towards a source of light above you. If you see any reflection then your knife is not sharp there.

Finally, don't put your knives in the sink, dishwasher, or drawer. These environments are all terrible for your knife edges. You're guaranteed to dull your knives considerably if you do any of these things.

Let me know if something still isn't making sense to you and I'll explain it. I know too much about knives.