You can't shut it down from Ctrl-Alt-Del. It refuses.
Apparently, that's so naughty viruses can't shut it down - although I've not worked out yet how they get in to start with if it's there and running.
Right click the Avast icon. Select "Program Settings">"Troubleshooting">"Disable Avast Self-Defence Module".
Once that's done, you can exit, then uninstall the program.
The bu@@ering around done first may have made that problematic. If so, go to the control panel, select Avast, and carry out a repair, following which it should uninstall OK. Use the uninstall utility next, or if that doesn't work, but you must stop protection and disable the self defence first.
[Edit] Just read the OP more thoroughly. (Sorry, just come off the night shift). The symptoms described fit with malware. Something has disabled your thingumy's.
Have access to another 'pooter? Dowload
MBAM to a disk or flash drive, try installing/updating/scanning with it.
Second prong, download
Cureit, don't update it (the download is the most updated version; it won't update), install it, scan with it.
The symptoms described also may fit with having more than one AV installed.