Answer to "Solution for distorted audio?"There are a few things that can cause your audio to stop working properly, and each requires a different fix. The first thing you should do is make sure that the holes over the speakers aren't just clogged. Look on the back of your phone, and see if there's dirt in the small line of holes near the bottom. If there is, running a fine needle through them should solve the problem. If that doesn't help, try making sure your software is up to date, because this might also be causing performance issues. If there still isn't any improvement, your speakers have probably blown out. You'll have to replace them.
Answer to "Capacitive buttons not working?"There are. The first thing you should do is ensure that your software is updated, as this can sometimes solve the problem. Otherwise, you can go to https://play.google.com/store/apps/detai..., and download what amounts to a patch. So long as the rest of your screen is working, it creates virtual buttons on top of where the capacitive buttons usually are. If this doesn't solve the problem, you may have to consider replacing the screen.
Answer to "Can I retrieve data from a phone with a broken screen?"If the screen is the only thing that's broken, its entirely possible to retrieve the data. If its just pictures you want to save, you can simply connect it to your computer, and download them off of the hard drive. All of your contact information and the like is stored on the SIM card, which will likely be moved to your new phone. If it isn't, you can ask the store to copy it for you. Everything is still stored on the hard drive, so you haven't actually lost anything by breaking the screen, though you could consider replacing the screen. It sounds like you may have a broken back-light, but its not clear based on your question. In any case, best of luck.