Based on your description, possible problems of the Canon A570 IS are:
- electronic fault;
- battery power or battery contacts.
The correct procedure would be to seek the services of an authorized service center (specially if the unit is still under warranty) or a qualified professional if it is an electronic fault.
Of the above, you could try to address the battery power by charging or replacing the battery as you have done / posted, or use higher rating batteries such as 2700 mAh NiMH batteries or Energizer AA 2500mAh batteries. Should the battery be known to be good, if haven't been tried and only if you would consider:
- clean the camera's battery contacts using Q-tips or cotton buds dipped in alcohol;
- in some cases, it maybe necessary to scrape these contacts to expose fresh metal;
- still, others would sometimes require that the contacts be bent or stretched a bit to ensure more pressure points to the battery.
Good luck and thank you for using JustAnswer.