Xperia Mini Display Repair
This vid shows how easy it is to exchange a broken display of your phone.
You can just order the replacement part and do it yourself. In this case i did it with my Sony Xperia Mini.
What happened was that it got wet and then I could see the water in the back of the display just before it stopped working. It did the vibration when turned on, but display was black. I assumed, that just the display was broken and I was right. Repair took 20min with explanations as you see and did cost me $15.50 for the part. This is way cheaper than a new phone.