Early 2013 MBP Retina 15 won't boot unless Thunderbolt -> Ethernet dongle plugged in
Troubleshooting is a process of elimination and often requires patience. This means trying things one by one until you get to the bottom of the problem.

The next two things I would try are running an Apple Diagnostics Test and also booting into Safe Mode. See below.

1. Run Apple Diagnostics

Follow the steps below to run Apple Diagnostics:


Fully shut down your MBP
Disconnect the Thunderbolt > Ethernet dongle
Restart your MBP
Immediately press the D key and keep it down until you see the Diagnostics screen appear
Wait for Diagnostics to finish (this typically only takes a few minutes)
Once complete, one of two things will appear on the screen:


a No issues found message
a brief description of any errors found plus further instructions

If the diagnostics test does find errors, take a note of what they are


Note: If pressing and holding the D key at Step 3 doesn't work, start again at Step 1 and, at Step 3 press and hold both the OptionD keys instead. This will try and run diagnostics from the internet instead, so you will need to allow more time for it to complete. If that still doesn't work, connect the Thunderbolt > Ethernet dongle and try following the above steps again (but skip Step 2).

Regardless, take a note of what happens.

2. Boot into Safe Mode

Follow the steps boot your MBP into Safe Mode:


Fully shut down your MBP
Disconnect the Thunderbolt > Ethernet dongle
Restart your MBP
Immediately press the Shift key and keep it down 
Let go of the Shift key when you see the login window (NOTE: If you have FileVault enabled you may need to log in twice).
Take a note of what happens (i.e. could you boot your MBP or not)
To exitSafe Mode just restart your Mac as normal


Once you've run the diagnostics and tested a boot into Safe Mode, let me know how you went and we'll go from there.