How to troubleshoot OTG cable? Because android doesn't handle the broken screen problem very well (frankly, it doesn't handle it at all) I bought OTG cable in hope that I'll be able to connect my mouse to the device.

I connected it to the broken phone (Huawei U8500) and nothing happened. Well, I tried my new android phone Samsung GT-S7710 with Android 4.1.2. However, still no effect. I tried USB flash disk, but that didn't do anything at all.

How can I debug the USB OTG function? To find out what's actually wrong?
Maybe try OTG Troubleshooter first to check if your setup is working:

https://play.google.com/store/apps/details?id=com.homesoft.otgtroubshooter

It will check if your device supports 'usb host mode', if your OTG cable is working and if a mass storage device is found.