Internet recovery mode cannot connect to wpa2 network

Without a recovery partition and (for whatever reason) your Internet Recovery just won't work, you are down to about 3 options to get OS X installed:

Option 1: Install (or Recovery) at an Apple Store

If you are close to an Apple Store you can go into one and download the latest OS (if you have a working Mac) or run Internet Recovery using the Apple Network.

Note: Internet Recovery will only install the last version you had, it won't upgrade. For example, if you had Mavericks before and want to go to El Capitan, you will have to recover to Mavericks then download the El Capitan Installer.

Option 2: Download and Make a USB Installer

This involves using another Mac from a friend, family member or acquaintance. You will need an 8GB flash drive. There are many guides on how to create the USB installer so I won't belabor that point here, but the command you will need to execute in Terminal is as follows:

sudo /Applications/Install\ OS\ X\ El\ Capitan.app/Contents/Resources/createinstallmedia --volume /Volumes/<USB Volume> --applicationpath /Applications/Install\ OS\ X\ El\ Capitan.app --nointeraction

Where <USB Volume> is the name of your USB Flash Drive (don't use spaces - it makes it easier)

After about 10 minutes you will have a USB Flash drive to install OS X on your Mac.

Option 3: Acquire a premade USB Drive

This is not an official recommendation but sometimes when you are in a pinch and Options 1 and 2 are simply not feasible, it's nice to know that there's another option. You can find these on eBay. I have used this option before when I had to restore a Macbook, Internet speed was slightly above dial up and the closest Apple store was in the next State.

Just make sure you you deal with a reputable US based seller with good feedback. If the seller is too new or feedback to low, look elsewhere even if the price is good.

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:

1. Shut down your machine. Yes, a full shut down, not just logging out.
2. 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.
3. Hold those keys down until your Mac reboots again and you here the startup chime.
4. 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:

1. Shut down your computer
2. Keep the MagSafe adapter (power cable) plugged in.
3. Press at the same time shiftoptioncontrol (on the left side of the keyboard) and the power button
4. Let go
5. 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.