After inspecting the iPad closely, it is clear that the underlying problem is the LCD layer. Although the screen reacts to touches, the display does not show properly at all. To fix this, we have to replace the LCD.

Luckily, replacement parts can be found online. In this case, it was actually possible to purchase the entire display (including all three layers), which makes the iPad easier to repair, since we do not have to reuse either the glass or digitizer from the current screen.

There are several resources available online, which will guide you through the process of replacing the screen, but iFixit is usually a safe bet. We also used their toolkit to perform the repair:

With the proper tools, it does not take long to replace the screen of the iPad; only around 30 minutes, in this case.