Alternative way to perform factory reset
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.