My RX10 will not turn on

@john76955 could be a DC-DC board issue. I would suggest that you check the voltage on your SY1027 board and check the F1 fuse while you are there. That is the same board that holds the RTC battery (replace that as well).

If you have power on that than you know that your battery terminal is good and the board gets power, Then you would need to proceed to the DC-DC converter and the power control IC. Luckily you can download the LVL 2 and 3 SM for your camera from this page Sony DSC-RX10 under the Documents Heading. Those manuals will help you to disassemble your camera and to check things out. Once you are at a point where you can check those things, post some good pictures of our boards etc. with your Question, here is the guide for that Adding images to an existing question That way we can see what you see.