Holding down the alt key stops some keys from working

If I hold down the (left) Alt key on my keyboard, a few - but not most - keys stop working. One of these is Tab, which means that it's difficult to Alt-Tab (not impossible - if I press Alt and then Tab in very quick succession it works). I used Key-Test to check what's going on. I held Alt down and pressed every key multiple times. The white keys below are the ones that registered. As you can see, a handful of keys would not press while holding alt, without any very clear pattern. I have tried the keyboard on another computer and got the same result (at least, Alt-Tab did not work). This is a

Question by Tom on Super User, licensed CC BY-SA. We show a short excerpt and link to the original thread as credit.