So it seems your hardware is OK.
Apparently, the UI is working to the extent that it can read the filesystem & interact with the hardware, but if apps aren't launching, it seems a piece of functionality is missing or broken. The clue may be the broken shutdown process - is this an app? Or is the process similar to launching an app?
I'm trying to think if there is anyway to launch an app without the launcher - maybe by detecting a captive portal or from Novaterm / command line? Oh, of course! Just type? Can you launch from just type? Do you get the keyboard? Also, when you write, 'desktops', I assume you mean launcher pages - which you presumably access from quick launch. Do any of the other quick launch items work?
Failling any of that, have you tried letting the battery go flat (I don't think you can pull a TP battery)? Then recharge and reboot? This might fix a temporary fault, but if not then we start to move towards reinstalling the OS...
P.S. You title is only one word, but reasonably descriptive - better than, "Help! My device is broken!"