First ensure that the charger to your cellular device is not the issue rather than the battery.
# Check to see if your phone charger works with another device that has the same charging cable.
# If this does not work buy a new phone charger because your charger has gone bad and is the reason your phone would not turn on.
However the charger does not seem to be the issue considering your phone turned off while it had a percentage of battery remaining.
# Remove your battery from the device in order to replace it with a new one.
# Replace the battery in your device with a newly purchased HTC one x plus battery
# In order to complete steps 1 and 2 follow the [guide|50026|battery replacement guide] guide for a detailed step by step process on replacing the battery.