Does Applecare cover a broken dock connector?

I have had my iPhone 3GS (Black, 8GB) for about one year and a half now. I did purchace Apple Care (regular, not +) with it. Yesterday, I tried charging it, but to no avail. Sometimes it says that it is charging but the battery percentage just drops, other times it just does nothing. I've tried a diffrent charger, but it still wouldn't charge. I tried connecting it to my computer. The phone syncs, but the battery percentage never goes up. Today, the phone doesn't even connect long enough to complete a sync. I was able to backup my info prior to this, but it is now out of battery.

What should I do now? Do I just walk into the store? I have never had an issue with my phone prior to this. I do not recall doing anything that could cause this. I have always kept it in good condition, and have only dropped it once, and even that drop was less than a foot. Will Apple replace the dock connector since I bought Apple Care? If they will, do I have to pay them to replace it? If Apple does agree, will they attempt to fix it, or will they just replace my phone with a refurbished one?