If the camera is completely dead try the following in this order:
replace USB cable (use the original cable if you have it. use mobile phone USB cables)
try different USB ports on different computers or different wall charges
replace battery (may break camera further. need to take apart camera)
At this stage, the camera is headed for recycle as a throwaway. So, you may want to try the following before the camera to electronics recycling service:
reflow solder on power circuit (using a heat gun may completely destroy circuit board)
rewire power delivery (at this point, you may have to use camera for parts only)
