In KDE4, by default, the application menu is invoked with the Alt-F1 keystroke while most in the subcortex have a button between Ctrl and Alt - Super, as it is also called the Windows button.
Unfortunately, the standard keyboard shortcut dialog allows you to use the Super button only in combination with another. Say Super only modifier and that's it. I haven’t been able to find a solution to this problem for a long time, the best thing I managed was to install Caps Lock.

However, today's Google, with the request “kde4 start menu super button”, brought a link to the
solution - a small utility ksuperkey.
For the assembly we need:
sudo apt-get install git gcc make libx11-dev libxtst-dev
We take source codes with github:
git clone https://github.com/hanschen/ksuperkey.git
We collect and run:
cd ksuperkey make ./ksuperkey
Hurray, it works! Super Super Super
According to the instructions of the utility's author, you must have the standard Alt-F1 shortcut set to open the application menu.
In autostart it will have to add hands.
Super → Applications → Settings → System Settings → Start and End (below) → Add Application.
Once again I will give a
link to the author's post.
UPD
It turns out that Gnome2 has the same problem - you cannot assign an action to the release of the super key. And, by default, the menu opens alt + f1 the program should work there too. Thanks
pawnhearts for the addition.