Can i back up all my files from Safe Mode ?

So my house had a Power outage and i got this massage:

"Connect a USB storage device that contains an update file for re-installation for version 4.07"

after looking around a little bit i understand that doing that will delete all my files.. is there any way to get them backed up from safe mode/HDD or something ? please help :/

Edit: here are some photos of my problem:

http://i.imgur.com/mGb9LwA.jpg

http://i.imgur.com/eQsq1Od.jpg

http://i.imgur.com/feJszeg.jpg

I had hundreds of hours worth of play time.. it will break me to delete them all :(

Thanks for anyone that help..