Iphone 4 shut down, won't turn on, won't charge and heating

Question

I have the iPhone 4 only for 3 weeks now, the first day I bought it, the phone restart automatically every 3-5 minutes when I plugged it in into the computer, did a hard reset, restore to original setting and upgrade and didn't work. So I send it back to the distributor to fix it - so there go my 1st week of iphone 4 purchase. After a week got the unit back, it was ok for about 10 days or so until 2 days ago, I noticed that the phone won't charge over the night when I plug it into the wall charger. And yesterday I placed it for a charge over the night, this morning I noticed the battery is only 22% and when i pulled out the charger it shuts down. When I plug it back in, it came back on again, however not charging, and shuts down again after I pulled it out. Same thing with the computer plug. Tried to hard reset, but won't work, won't even turn on. So I plug it in and ran the BatteryDoctor app, it seems to fix the problem as it start chargin again, although my Iphone got quite warm in this process. That was morning. Now, the thing shuts down automatically, though the battery was still 40%, did a hard reset and won't work. So plugging it into the computer, it came back on, and again shuts down when it is pulled out, however this time hard reset works. This is starting to worry me. Is this a hardware problem?? I some threads that  people are having a shut down problem also. HELPPP!

Answer 1

Ok, so I went to try that and run the program it said I needed .Net Framework 4.0 installed, so I was on my way to update that so I could try to run the program.
Anyway, before I did that, a coworker comes by and I show her that my phone is dead. I unplug it from my computer (it's not charging or anything) and I start pressing the power button rapidly to show her it's dead. All of a sudden the screen turns on and shows me that the battery is drained and needs to be recharged. I quickly connect my phone back to the computer and it begins charging. After a few minutes the Apple logo appear and it is detected on my computer! It is currently charging and is seen in iTunes. All is well again.
What's weird is that I know for a FACT that the battery was not dead when the update was done. In fact the phone showed FULL battery right before I unplugged it the first time.
I don't know if it was a combination of the steps above or what, but whatever it was, I appreciate everyone's input.