Keys all switched on keyboard
For the simple case, it sounds like you have a different keyboard layout (e.g German, as that swaps Y and Z).
Change layouts in Control Panel:
- "Clock, Language, and Region"
- "Region and Language "
- "Keyboards and Languages" tab, -> "Change keyboards"
Press Alt-Shift to switch layouts.
However this does not explain function keys. It's possible to arbitrarily remap keys using the registry. I think you'll need a 3rd party tool to fix this. Example: https://sharpkeys.codeplex.com/
Remember you can use the "On screen keyboard" (Start Menu\Programs\Accessories\Ease of Access\On screen keyboard) to type with the mouse.
If you don't want to use any third-party applications to reverse the SharpKeys modifications, you can cut out the middleman and edit the Registry directly.
Open the Registry Editor by navigating to C:\Windows\regedit.exe in Explorer. Once it's open, navigate here:
HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Control\Keyboard Layout
If there are entries called Scancode Map or Value Scancode Map, delete them. Those are what cause Windows to remap incoming keypresses from the keyboard.
Once you're done, reboot. Key remappings will be reset to the default. You can do all of this with the mouse only, no keyboard.
References for those IDs: Main.cs in the SharpKeys source code, "How to Disable the Insert Key in Windows" from WikiHow.
It's worth checking for processes running in the background which manipulate your key entry. I use AutoHotkey scripts to add/override some keybindings. They generally appear in the system tray as a little green icon with a capital 'H'.
If you can't find the process there, you can also check the 'startup' folder in your start menu to see if they have added something to run when you log on.