1)Check if you charger is working on a different Nokia mobile, sometimes the charging doesn't work and tricking you into thinking your mobile phone is faulty.
2)Hard reset the Nokia c7.
2)You can't update the firmware on the c7, when the Nokia c7 is switched off. So i suggest you use JAF a great flashing tool, to flash the firmware of the c7 in dead usb mode. On most occasions, many Nokia phones that i have come across, fail to power on because of faulty firmware.
3)Replace the power button.
3)Replace the battery pack.
3)Replace the charging block.