Alternative way to perform factory reset My friend's daughter was playing with the unlocking screen and of course she used up all the attempts and locked the device for good. Since this tablet was bought some time ago just for her amusement, no one remembers what was the google account they used - possibly a phony one created just for the purpose of using the device. This discards google recovery as an option.

It's a cheapo tablet sold here by Walmart under ONN brand. I did some research and have found it's being made by YiFang Digital and marketed as M7000NBD 

http://www.yifangdigital.com/product/M7000NBD.aspx

According to the manufacturer, it's powered by AML8726-MXS Dual Core + Mali TM-400 and it's running Android 4.2. Unless it came like that from the factory, it's not rooted, and it has only 3 buttons: PWR, VOL UP, VOL DOWN.

My friend doesn't care about the data stored on this device and I offered to help thinking that I will be able to perform a factory reset the usual way. I was wrong.

When I use the PWR + VOL UP key combination, to enter Android system recovery, first thing that shows up after the boot is an Android figure with a red triangle and an exclamation mark. If I press the PWR+VOL UP again, the system recovery menu shows up but I can not navigate through its options. At least not using the VOL UP/DOWN buttons. 

The only button that works is the PWR, but since "reboot system now" is the option selected by default, it's the only action I can perform from within this menu.

When the above failed, I thought about ADB as an alternative way. Unfortunately the USB debugging seems to be turned off so, as far as my limited knowledge goes, there is no way of running ADB shell in that case. For obvious reasons, there is also no way of switching it on.

Is there any other option to factory reset this device? Or maybe there is a way to make the system recovery menu respond?

If it makes any difference, I have a Windows 7 desktop and two notebooks running Windows 8 and Ubuntu 13.10 respectively.
I think you should take a look at fastboot commands. Fastboot works in bootloader mode even when phone is not switched on in Recovery or ROM or even if Android isn't installed on phone. In later case, bootloader can be accessed by certain button combination while powering on device; usually Power + Vol Down. Though ADB is more flexible, but in your case it is out of the question.  

What you can do now is :
Step 1: Unlock the Bootloader
Step 2: Flash a Custom Recovery (like TWRP)
Step 3: Flash a custom ROM that you want
(For detailed steps and commands, visit: XDA-developers)

Beware that some original ROMs can't be flashed by custom recoveries that's why i suggested a custom ROM in step 3.  

After that reboot your device and turn on developer options and ADB in that new ROM. Now you can reboot to recovery and access ADB to flash your original Recovery and ROM through ADB commands.

A bit lengthy but it has always worked for me.