RCA MBT0004 4GB 5V32JD MP3 player won't turn on.

My MP3 player won't turn on. It plays when connected, but otherwise won't turn on when connected. I've had this problem with it before, took it back, got another one at no cost, and now this one is doing exactly the same thing. I never let the battery die, but it still won't turn on. How do I troubleshoot it without smashing the damn thing? I don't want to have to go buy yet ANOTHER MP3 player. If I could afford one, I'd get a better one.