New battery and headphone jack assembly? Did the problem start right after that? If it did, I'd suspect that someone broke something, left off a connector, pinched a cable, something like that.
If not, and if you can work on it yourself, it may pay to try to reflash it.
At any rate, don't toss it. If you want to get rid of it, find a local phone repair shop and ask if they want it for parts. (Get friendly with them and give them your old, no longer needed phones and tabs, and in the future if you need a little favor you can ask for it. [It's how I ran my cellphone stores - you help me and I'll help you.] At the very least, they can use it to train a new tech on replacing the glass on a screen. He's going to break a few before he learns, and a phone or tab that doesn't pay to repair is handy if he's going to break it anyway.)