iPod showing bluescreen and shifted display

My five year old ipod classic (80 gb) frequently ends up with bluescreen (well, white screen, it´s apple). If i restart, it keeps on working a couple of minutes before running out of battery. If I connect it with my MacBook, the battery starts charging – synchronizing is also possible. But when I disconnect with the battery icon saying “full”, the battery status goes to zero within minutes.

There`s also a new problem with the displayed image. It looks like shifted to the right, part of the image looks like cut up on the right side – this little part reappears on the left side of the screen.

Service personnel at the Apple Store once told me the harddisk was broken – the next day another technician found out it might be a system error. Strange…

Maybe i just change the iPods battery?

Greetings from Berlin,

Lukas