Ok, my daughter cracked her screen recently. She has been having "software" issues as well, Genius Bar tells her to restore to new and manually install apps and music again, they thought backup had been corrupted. This did not solve her problems. We went back to Genius Bar Sunday morning they looked t her phone and decided it was still software based, and the restore she did could not resolve this. I then told tech I would like to get screen fixed by third party, but did not want to void warranty. He agreed that would be a bad idea, and stated cracked screen has nothing to do with software issues. My daughter walked out with a refurbished phone.
if you have a store close by vist them a few times after restores and I'm sure they will give you a new phone. Good luck.
P.S. phone is still under warranty correct?