Will Apple fix my LCD screen under warranty?

I have an iPhone 4s, that I bought around a month ago. It is under warranty. I have been having issues with the phone since the day I received it in the mail. One being that I get dial tones and/or other static-y noises at the beginning of all outgoing and incoming calls, usually for about 2-3 seconds. The phone also randomly dies, even if it has 15, 20 sometimes even 30 percent battery left. The biggest issue I've ran into is the front screen of the phone popping off. Not completely, but enough to notice. The way I can tell when it happens is because the home button will feel weird, like majorly indented and then light can be seen coming out through the side of the phone. The problem is that each time this happens the screen would get little crack-looking disturbances or just discolored all over, and then tonight it popped out AGAIN while I was talking to my mom and then screen went black and the phone just started making a weird bonging sound over and over. For lack of a better term, I'm pissed.
The phone itself is perfect. No scratches, no dents, nothing. It's always been in a case.

My husband is adamant that I'm wasting my time because Apple will not replace an LCD screen, but obviously the phone has had issues since I received it and it's not anything that I did! I spoke to a very nice representative who made an appointment at the Apple Store to have it checked out. Has anyone had any luck with getting something like this taken care of under warranty?

No claim for broken damaged parts

If you have broken something, you need the Apple Care plan. Otherwise it is highly unlikely they will fix it for free.

That's my point- I *haven't* broken the phone. It's never been dropped or anything, there's not a single scratch on it and it's always been in a case. I'm aware they don't cover "accidental damage", if that were the case and my only concern I'd go right down the road where I live and pay $50 to have it fixed instead of making a 4 hour drive to the Apple Store. There was NO accidental damage, and the screen is only part of a series of issues the phone has been having since coming out of the box. I've been an iPhone user for years and have never had such issues with a phone!