Well I hate to be an alarmist, but windows update not working and AV program stops working at the same time sound like a Malware attack of some sort. Without updates and any antivirus software working your system is wide open to further exploitation. Check to see if your firewall up and operating.
I would start by backing up my data if you do not have backups already, then try a system restore to see if you get back control of the system. A system restore will NOT
remove Malware, but it could get the Updates and AV software working again, and give you some control and protection.
If you can't get system restore to work,install a anti virus program and/or the firewall is off, get on a second computer and download Karspersky TDSSKiller and run on your troubled PC. You find it at this link Karspersky TDSSKiller
. It runs fairly quick and looks for rootkits. Then download Malwarebytes free version on the second computer from here Malwarebytes
. Then run it on the troubled computer as well.
Also, if you can get AV install and some control back, you can run a on-line scan at ESET Online scan
Let us know how it goes. Many forum member are very skilled at removing tough malware, so you came to the right place.
Hope this helps.