It died during a conversation and now will not turn on

From the sound of your post it seems either fully flat or the battery has really died. When you say "plugged into my charger for at least 12 hours" I hope that you mean to the wall? If you say yes on that one, then is that into a power board, or directly into the wall? Have you tried a different charge cable? They break internally very easily and can cause many silly problems. A fully flat iPhone can only get going from mains power, and depending on the state of your battery a power board may infact still not give enough juice to kick it into life.

If that still yeilds no result then it is time to throw in a new battery. You can purchase directly through ifixit.

iPhone 4 Replacement Battery

It is the simpliest repairs of them all. To do anything else requires the removal of the Battery. If you need some guidance on how to actually do it then this link should help you, there is even a video for that extra bit of visual stimulation.

Installing an iPhone 4 Battery

I hope this helps you get life back into your beloved iPhone.

Good Luck.

Deano