Trash?

Question

we have this memorex mmp8640 and you can charge it all day, only thing plugged in, it will turn on. you can listen for 5 min or 3 hrs but as soon as you turn it off it wont turn back on until you charge it again... their tech support sucks! they said to try downloading the firmware but I cant find it anywhere. Target wont take it back and they want to charge me 70 bucks to send it in. I dont want to pay that for a nother if it didnt last a yr the first time. Is there any help or should I face the facts.
Thanks