Once I uninstalled and installed Avast 5. 0.507 Windows Security Alert window has not come up since, but I have not rebooted either however I still can't update either automatically or manually. This is serious!
Well technically the WSC is correct as you had 5.0.462 and the latest version is 5.0.507, now you have done that, hopefully that issue is resolved.
You don't mention what the virus definitions version is, latest is 100420-1 ?
You have to reboot after the reinstall/update to 5.0.507 as many elements may not work until after a windows restart, so reboot as Asyn suggested.
After a reboot try a manual update a little while after windows has started as avast checks for updates once a connection has been established. Try any sooner and you may bump into the avast update is already running error.
If the manual update error is displayed, check the Task Manager and see if avast.setup is already running, if so it looks like an auto update is being attempted at the time (or has stalled).
But lets reboot and see what happens after that.