First, all the ideas that come after this answer are great. Use whichever one works for you. These are important, and my next tip should only be a supplement to those.
Second, and what I do, is flex. Whenever you're thinking about it, just flex your abs. For example, as I'm typing this answer I'm flexing. When you're in school or at work, just flex under you're shirt. Nobody knows you're doing it, and it works. It's not amazingly fast, but it works. I did this all summer. When I'm at the pool (and I'm there a lot) I have to take my shirt off, so there's a good time to just start flexing your abs. What this does is contracts your muscles. Muscle tone is just a constant contraction of the muscles that becomes involuntary. The more you do it, the more you are training your abs to stay that way. This is literally what you call "muscle memory."
When you have a bad back and want abs dont do sit ups or crunches as u can see ur not getting results. I have been using the " Bender Ball" and I have gotton such great results and I am only 11 years old!
When you have a 'bad back' it is often because you have not developed your abdominal muscles. In fact if you develop and use your abdominal muscles correctly, you may well cure your bad back.
I recommend Pilates to you as it teaches you how to use your abs to support all your movements from a 'Stable centre'and without putting unnecessary strain on your back.
I am a body builder and a few years ago ruptured a disc in the lower back. with my bad back i cant do the regular situp. but can do the more effective slow crunch, also you can lay on your back and do leg lifts, both legs at the same time is too stressfull on the back so I will do one leg at a time while the other is drawn half way up with the foot planted on the ground for support. also it can help to place your hands flat under your buttucks, this takes stress off the lower back as well. your best bet is to stick with slow crunches holding at the top for a second on each rep.