iPhone 4 won't turn on completely..?

Recently, I dropped my iPhone 4 and now it will not completely turn on. When charged, it will show the Apple logo, as if it were turning on, and then it will show a gray/black screen... Occasionally, it will turn off, and I've let it die several times, but it will not turn on. A hard reset has not done anything, and I have a hard time putting it into Recovery mode because my lock button is broken. I've also connected my phone to the computer, and iTunes will recognize my phone, but when I allow iTunes to access my information, it says "to allow access, please respond from your iPhone...".

I'm really only worried about saving my pictures... Is there any other way to access and save my pictures? (My phone has also not been backed up with iCloud either, and the last time it was back up with iTunes was in November 2013...)

If I can put my phone into recovery mode, will I lose all of my data?