On the Rpi3, you should get a steady red light. That indicates proper voltage.
Then you should get a 2 second green light as it mounts the SD card.
Then after a few seconds there should be a steady green then some flashing as it boots.
===> If you are not getting that steady green then it is not booting.
===> If you are not getting a steady red then the voltage is too low.
Sometimes, during boot, it will activate a device, maybe even a USB WiFi adapter, which pulls the voltage just low enough that the boot process can't complete yet the red light stays on.
The test for that is to pull out the WiFi adapter and then see if the system will boot up. Then when it shows the solid green for a while you can hot-plug in the WiFi adapter.
If that's the case then I replace the power supply cable to eliminate that as a cause.
Always make sure you have good image backups of your SD cards, using Win32DiskImager.