Unable to enter Recovery Mode -2006F
Considering you can't boot into an OS, the first things I'd try are resetting the NVRAM and SMC. Below are the steps for doing so, as well as the order you should do it.

1. Reset the NVRAM

Older Macs had what's called Parameter RAM (PRAM), newer Macs use Non-Volatile Random-Access Memory (NVRAM). Here’s how to reset it on your particular Mac:


Shut down your machine. Yes, a full shut down, not just logging out.
Press the power button and then press the commandoptionpr keys. You have to make sure you press these keys before the gray screen appears or it won’t work.
Hold those keys down until your Mac reboots again and you here the startup chime.
Let go of the keys and let your Mac reboot normally.


Note: When you log back in you may need to readjust some of your system preferences (e.g. speaker volume, screen resolution, startup disk selection, time zone information, etc).

2. Reset the SMC

Here’s what you do to reset the SMC on your particular Mac:


Shut down your computer
Keep the MagSafe adapter (power cable) plugged in.
Press at the same time shiftoptioncontrol (on the left side of the keyboard) and the power button
Let go
Turn your computer back on with the power button.


Once you've done both of these, check to see whether the problem behaviour (i.e. an inability to enter Internet recovery) is still present. Let me know how you go.