IPhone dead

Ok, I know there are lots of Questions about this ..... but

I have an iPhone 4, running IOS 6 

The phone has reset a few times, mid conversation, which was a pain.

Last night, I plugged the iPhone into my MacBook Pro to charge, I saw the picture of the battery come up, so it appeared to be charging.

This morning, the phone is completely dead!

I have tried

1. Plugging in the phone using various Apple leads (they all work with iPad and iPod) iPhone not recognised in iTunes (Although when plugged in, it initially freezes the mouse on the MacBook - I have restarted, and switched off / on MacBook)

2. Plugging into different ports on MacBook

3. Using different power adaptors (they work with iPad and iPod)

4. Trying the hard resets that have been mentioned in this community

5. Attempting to find something on the Apple site - all seem to point to updating software, which can't be done, as the phone is dead

So some questions

1. Is the phone toast?  should i get a replacement

2. How the **** do you contact Apple support, if your phone doesn't work? can they be emailed?

3. Is there a way around this - I have even tried speaking nicely to my iPhone

Many thanks