HC-05 BlueTooth Module: Unable to enter AT mode

For a groupswork we have acquired an HC-05 BlueTooth module.
When powering up the module, a Bluetooth connection with name ing-xxxxx (xxxxx being some numbers) shows on the screen. The standard passwords 0000 and 1234 seem to be incorrect.

Therefore, I wanted to boot the module in AT mode. I tried pressing in button and afterwards connecting power. The onboard LED keeps blinking 5tps.

Then I tried connecting 3.3V to the KEY/EN pin. This also fails.

Then I tried connecting 3.3V to the 34th pin of the module itself. On power on, still in data mode.

As final test I repeated all 3 option, and connected a led to the 34th pin, just to see if there's an actual voltage applied. What turns out: Yes the LED burns, in all 3 cases, yet still does not enter AT mode.

Is my module broken?
Am I missing something?

Thanks a lot!

It's easier if you use the on-board pushbutton to put the HC-05 into AT mode.

Also, please post your code and your schematic. Also, can you link to the module you bought? (sometimes people mix up HC-05 and HC-06 modules)

BinaryFour:
Is my module broken?
Am I missing something?

Quite possibly yes to either or both.
Your description implies the module is either, not new and has been reconfigured, or the passwords merely seem incorrect to you, but are in fact OK. It may be that the xxxx you are so secretive about is in fact the password. It may also be that you have simply wired Rx>Tx and Tx>Rx the wrong way round.
Check the Martyn Currey website. he has good words, and pictures, on this matter.