i have a 2nd generation after i backed it up a couple days later it wouldnt turn on

i have a 2nd generation ipod and my computer said i didnt install itunes right so i cant burn cds or transfer music to my ipod. but i wanted to back it up so i wouldnt lose the songs i just bought. in the pat i have boughten music from itunes and it just deleted off my ipod. so now all my music and stuff is in itunes but i cant transfer it on.anyway after i backed it up the song i transfered skip over and they wont play. then two days later i was charging it on a wall charger overnight and in the morning it completly turned off and wouldnt turn on no matter what i do. then i plugged it into my computer and itunes didnt regonize it. what can i do to help it turn on also will i get a refund or something. plus if i buy a new one and if i re install itunes will i have all my apps and music saved.