I can confirm now, that this problem is not connected to picking up items when the inventory is full. Skills can be used freely if the inventory is not full. Additionally, ever since I posted this thread, I have had several occurrences of ignored keystrokes all the while there were no items in my surroundings.
Any other ideas? :(
You should really grab a good keyboard with at least 6 key (NKRO) for gaming in diablo 3, there are many, but basically what could be happening is a hardware issue. If you press to many buttons at once the keyboard actual locks on to repeat a keystroke multiple times and prevents other keys "keystrokes" from being sent. A complete review of what happens and why is here.
Please take the time to read the full article and some of the reviews. As to a recommendation. For diablo 3 bare minimum 6 key (NKRO) these keys should include 1,2,3,4,5,6,7,8,9,0,w,a,s,d,q,e,r,t,f,g,z,x,c. You know the most commenly used keystrokes in gaming.
I wont say that it is your issue specifically, but I noticed significant improvement on my keystrokes being sent when I picked up my new logitech g710 usb 2.0 keyboard.