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Thanks for answering my questions.

So with no headphones plugged in you get no sound through the built-in speakers on your iPhone.

Based on the screen shots you posted it looks like your phone thinks it's connected to a dock connection. That's jives with your "sound in headphones, no sound from internal speakers" answers to my questions.

It sounds very much like your dock connection at the bottom of the phone is not functioning correctly. It may just have some debris in it that's shorting out a few pins and making your iPhone think it's connected to a dock with a line-out on it, or it may be completely broken.

Try cleaning out the dock connection jack on the bottom of the phone. You can blow in it with a dry air source, compressed air in a can is best, to see if you can dislodge any debris from it. You can also try plugging your dock connector in and out a few times to see if that clears it up.

If that doesn't work your best bet is to take it an Apple Repair Depot and have them look at it. The dock connection is made up of a lot of small terminal points and it's not hard to mess them up if you force a connector in the wrong way or smush some debris in there when plugging it in to charge.