How to recognize a defective WLAN module in the laptop?

Suddenly the wlan of my laptop (Sony Vaio, without mechanical W-Lan switch!) Is no longer. In the Windows 7 Device Manager Prof. Only a "Realtek PCIe GBE Family Controller" but not an Intel Wireless Controller is listed, even though its driver and associated software properly install and display the Intel Wireless Control Center that enables Wireless Connection, that is, all in all ok.
With the Windows Troubleshooting I turn unsuccessfully in the circle, because they always only reports that there's a cable error and I should please plug the LAN cable.
Under "Network and Internet Settings \ Change Adapter Settings", only the above mentioned Realtek Controller is listed.

So for me that looks like a hardware failure of the wireless module, what do you think?

Is the WLAN switched on via the control panel (Windows key # I)?

Try the following:
Click an empty spot in the Device Manager> Menu bar: "Action"> Search for changed hardware…
After a few seconds, the wireless adapter would appear - if it is technically in order and not hidden hidden.
Then download the (Realtek?) WLAN adapter driver and install it.

Yes.