Just thought I'd let you know that this happened to me too, I had it 5 days and then it did exactly what you said- there was noise for a few seconds, then it'd go dead yet the green light would be on. I tried using more oil (I use stretch mark oil as anything liquidy works !!), and even tried new headphones like you but it didn't work. My parents eventually popped round to see me and brought me some new batteries, and then it worked !!
The thing is, you should've seen the state of me when it wouldn't work haha ! The instructions say not to bash it or it'll break, and when I was in the car the other day, I had it in a bag on the seat and I smashed onto the floor as we came to a roundabout. I was convinced I'd broken it, and my hormones made me have a sobbing fit ! XD I called OH and was going 'oh my god, I've broken it already ! I've had it 5 days and I've broken it ! How can I look after a tiny baby when I can't even look after a piece of equipment ? Oh my god I'm uselessssss ! :'(' hahahaha. Thinking about it now it's hilarious, but I was in pieces at the time xD !!