Is it possible for a virus to cause the PC not to start
possible yes, but viruses like computers to run, so it can do what it was designed for......like steal your bank info, depending on virus type....
....prevent Windows from updating?....
yes if those updates will make it difficult for the virus to do its work....again depends on virus type
Can viruses also prevent Anti-Virus software from updating and running?
absolutely, again depending on virus type it will try everything not to be killed
(found in virus chest of Panda Anti-Virus, a previous anti-virus I thought had been removed)
Viruses have been detected inside Panda Antivirus files https://support.avast.com/index.php?_m=knowledgebase&_a=viewarticle&kbarticleid=53&nav=0,1,23,24

so you should run Pand Removal tool found here #29a http://uninstallers.blogspot.com/