What to do when my screen stay white?

Dominic, for what it will cost you to ship it to get repaired, you might as well do it yourself. I would start by opening it up and checking the display connector. the white screen only means that the backlight is working, no data. If your cable and connector are okay, replace the display. Not a bad job, but it will require you to properly identify your iPod. the displays are different even so the task is the same. Use the guides from here to get it done. Hope this helps, good luck.