Xseries :: Nokia X6 Won't Turn On - Any Way To Still Backup Files?

I wanted to backup my phone last night, it has several irreplaceable pictures and videos and today the phone seems to be dead. Last night, it was working fine, I closed any apps I had running, set the alarm and locked the phone. I wake up late today to find that my phone isn't working, I try unlocking it, taking the battery out, charging it. Nothing. I can't get it to turn on. Any way I can back up the files that are on there. Presuming it's not the drive in the phone that is dead, the files are still there and can be recovered, but I doubt Nokia support would go to that effort and they'd probably just give me a new phone. I want those files more than I want the phone.