Google Nexus 5 — Nexus Data Recovery

I dropped my Nexus 5 from a rollercoaster ride and now it is severely damaged. Surprisingly, the screen didn't crack but it is not responding, and when it does, it only displays a band of white thin lines on the left side of the screen. It seems to still be vibrating to notifications received from social media, text messages etc.

I was wondering whether it is possible/feasible to get it fixed, or, if it's not, to at least recover the data I have on the phone (Pictures, Videos, Notes and other files)