Is there any way to capture a manual log? Or does the fact that no log is created mean that LE doesn't even manage to start...
kodi.old.log shows a successful boot sequence, so it's not helpful. Maybe a broken hardware part, which can't be initialized at boot sometimes. Hardware boot sequences are complex, so random results are possible.
You can search for dead hardware parts after successful boot (internal WiFi, Bluetooth etc.). I don't think it's an LE problem.