Two main issues may have happened to your [URL=http://www.forevermac.com/category/apple_iphone/ |iPhone]:
1) A Dead battery, which means that it simply won't even hold the date/ time. There's always a small amount of charge left in the battery that ensures it maintains the date/ time. I suspect this is fed by battery and not the actual charger- hence it won't power on properly from the mains. Replace the battery.
2) The Power Management unit is corrupted/ your OS is corrupted. Far more unlikely.
I would replace the battery to see if that fixes it.