really strange iPhone 4 problem

I have an iPhone 4 that will shut off randomly by itself. I then can perform a hard reset on it by holding the power and home buttons at the same time and it will restart. It will do this a few times and then after the 5th or 6th time it will just go completely unresponsive. I have to wait for the battery to full drain while the phone is off (which if it has half a full charge on it takes 2-3 days) and it will come up with the "I need to be plugged in" screen. It will charge and work for a while and then the whole process repeats.

I don't have the money for a new phone. Please help!