Have you tried an alternative RPI3 power supply. It may be failing giving you intermittent problems.
I've tried different power supplies, and actually different RPI's. All points to this one being faulty, but before throwing it out, I wanted to do a bit more exact troubleshooting. By method of elimination, it looks like a HW fault.
- SD card with new image works with the same PS, HDMI cable and monitor fine.
- this RPI doesn't display anything at all with 2 different power supplies and 3 different SD cards with 2 different LE images