Well I would say the "every five seconds some alert or warning about malware, virus' or other dire gloom or doom things were popping up on my screen" comment I believe indicates a rogue scamware and do not come from avast. So a screenshot would help of the alert. This is known as a fake alert.
Unless of course if you are in the same slight over exaggeration about the comment "or other dire gloom or doom things were popping up on my screen" which is a very common trait on these fake alert, rogue scamware. The are inviting you to visit a site, etc. to have a scan done, etc. etc.
So we do need some clarification ?
Black screens, enlarged screens, blue screens aren't the preserve of avast.
If you haven't already got this software (freeware), download, install, update and run it,
preferably in safe mode and report the findings (it should product a log file).
1.
SUPERantispyware On-Demand only in free version.
2. MalwareBytes Anti-Malware, On-Demand only in free version
http://download.bleepingcomputer.com/malwarebytes/mbam-setup.exe, right click on the link and select Save As or Save File (As depending on your browser), save it to a location where you can find it easily later.