iPhone 4 Doesn't charge well, warm up, 6hours of use

hi everybody,

I leave in republic dominican, I'm french and repair Iphone since 5 or 6 years ago. I'll try to explain my problem the best I can with my poor english so sorry for differents mistakes...

I have an iphone 4 who works fine BUT:

-when the battery is empty and plugged to charge it, it does't turn on (just apple appear then turn off and try turning on by itself with apple logo)

-when I charge the battery with an other iphone or change it with a charged battery, it turns on and can be a usefull idevice

-when I plugg it with a 5-6% charged battery (in computer or wall charger) it warm up but charge until 100%

-when I use it with a 100% charged battery,it's usable for about 6 hours until the phone turn off (battery at 0%) and warm up when when I use it (turn on the screen, give a call, use internet on wifi or 3G...)

-the part who warm up is on the logicboard near the battery connector is called 36MY1EF (http://hpics.li/31947f3)

#1 36MY1EF

http://img15.hostingpics.net/pics/431358...

#2 power IC mangement

http://img15.hostingpics.net/pics/738279...

#3 small power IC, looks like good

http://img15.hostingpics.net/pics/373991...

#4 USB charger IC 75202, looks like dead

http://img15.hostingpics.net/pics/213197...

#5 don't know what is it but looks like burned

http://img15.hostingpics.net/pics/794255...

all pics are from my idevice

My question is: am I supposed to change just the USB charging IC situated near the USB port connector (#4) and power IC management (2), or other parts?

thank you for your help