Hi Karlyn, there is a pretty long list as to why your camera will not turn on including what you mentioned, the power button or batteries. To keep things simple at first inspect the battery compartment for signs of damage to the contacts and perhaps corrosion. How old are both batteries ? The likelihood of both batteries being bad is slim but possible. If you have the ACK-DC20 power adapter you can try that and see if the camera turns on...that would narrow it down.
Also be sure the battery compartment door is closing properly and not damaged, the camera will not turn on if it is not closed completely.
Next your looking at an internal fuse or circuit board issue which would require service. Or perhaps the power button also. I did a quick search on the G9 with Google and saw multiple You Tube videos and "hits" with the same problem you are reporting and how to repair it...depending on how brave one is lol !
