Logs can be found on the core server system under YourDrive\ProgramData\Paessler\PRTG Network Monitor\Logs. For example your Core Server stopped running, you will find logs about the Core in the directory /core. The ProgramData directory might be hidden in your file explorer. Go to View and check the box Hidden Items. The directory should now be displayed.
For more detailed information about how and where PRTG stores its data please see here.
Disclaimer: The information in the Paessler Knowledge Base comes without warranty of any kind. Use at your own risk. Before applying any instructions please exercise proper system administrator housekeeping. You must make sure that a proper backup of all your data is available.