I have been getting the same problem over the last five days. I have tried resetting (home and top button together) which sometimes helps for a while, but without that it keeps cycling to the Apple logo.
After a couple of goes at that I did a full restore, with better functioning for a short while, but I have now identified that whenever I try to watch video - sometimes after 10 - 20 min, sometimes much sooner, the screen flashes to a stripey white, then black, then the logo, and just stays there. Resetting, waiting a while, then restarting can allow me to use other apps, but if I start up YouTube, or the video player, pretty soon the flash to black occurs again.
Time to go to the Apple Store?