Try Restore of iPhone with iTunes 10.7 or 11 on computer. See if fixed. If still problem, and there is Warranty or AppleCare, make Genius reservation and take to Apple for resolution. You can try Virtual Home Button if you want. Tap Settings App > General > Accessibility > Assistive Touch > ON > tap new small white screen button > Home.
I recently installed iTunes 11, & just got back from vacation so didn't install ios 6 before I went (didn't want the issues I'd heard about), & when I came back 6.0.1 was available. Thinking this would be better I let iTuenes install this w/o ios 6 first (don't know how to do that if I wanted to). I haven't been able to find anywhere how to go backwords or even how to download the ios's w/o software update & that always gives you the lastest one.
I think I'm gonna start up from an older backup drive w/ 10.7 & see if I can do a restore w/o an upgrade for now.
I've been messin' w/ this all day & it's getting old, though I would like some of the features of 6 & presumably the fixes in 6.0.1.