put in freezer overnight. take out and install battery and it will turn on. sounds crazy but it worked for me. something to do with the electrical contacts inside contracting and possible breaking dielectric corrosion in the process.
Try cooling it in refrigerator over night, then install battery and turn on. Worked for me! It defies logic but was last chance before I tore into it and checked C11 on mobo by lens as directed by another user. It's a 47mfd tantelum surface mount cap (476) that failed on another user. I'm not sure if it was the temperature or the drying effect of the dry refrigerated air that did it.
That pad looks like a ground to me. See the large blue trace? Thats usually a ground plane. Just bridge the pad that is left to the ground or put a jumper between 1 and 3 off what is left of trace. 4 and 5 look common as well. Use flux as solder wont stick as your working with it well.
Drop camera in deionized/distilled water without battery. This will hopefully clean the camera insides including the lens element that has fogged. Remove camera, drain for 1 day over paper towel rotating every once in a while to dislodge puddled water. place in oven at 150F for 30 minutes on hotpad so it doesnt get full heat of metal contact. Next, place camera in bag of rice or other desiccant for a week, ou cna put in fridge too as that air is very dry. After you take out of fridge, warm to room temp for a few hours and then you are ready to cross fingers and put battery in. If all goes well, your camera will come back to life. The lens may still be dirty but that is a physical cleaning operation.