No, there is no way to fix it without restoring it which will delete everything. It would be better to take it in to your local Apple Store to see if they can recover your data for you while they also fix your phone. Use the link below to set up a Genius appointment at your local Apple retailer.
- Try to backup and and then import the photos into your computer
If yuu can't do that then likey the contents of the iPod are lost.
When it says place the iPOd in recovery mode use one of these programs.
- If not successful and you can't fully turn the iOS device fully off, let the battery fully drain. After charging for an least an hour try the above again.
- Try on another computer
- If still not successful that usually indicates a hardware problem and an appointment at the Genius Bar of an Apple store is in order.
TRY A THREE FINGER DOUBLE TAP ON THE SCREEN...
This worked for me as my magnification can be screwy at times, and zoom in all the way to the point where I don't even see anything.
I honestly can't believe this hasn't been mentioned... go to the screen when it lit up white and use 3 fingers simultaneously to double tap the screen.
Could save you losing everything and buying a whole new phone, for something so easy a fix.
Again, you're white screen problem might be something else, but its worth a try.