Windows won't update

I recently found Windows update hasn't worked for some weeks.
This morning I tried again - eventually got as message saying I need a new version of the updater. The message said that if I did as instructed, windows updater would close and then re-open. It did indeed close, but failed to re-open.
I have scanned for malware (I have Norton 360 running, and also checked with Malwarebytes, and Windows own emergency scanner) but my PC shows clean. Repeated attempts to do an update get me nowhere, and Microsoft's automated tool, which is supposed to fix this sort of thing, isn't helping.

Can anyone suggest where I go from here, please?

Tech Support Guy System Info Utility version 1.0.0.2
OS Version: Microsoft Windows 7 Professional, Service Pack 1, 64 bit
Processor: Intel(R) Core(TM)2 Duo CPU E8500 @ 3.16GHz, Intel64 Family 6 Model 23 Stepping 6
Processor Count: 2
RAM: 4028 Mb
Graphics Card: NVIDIA GeForce 8600 GT (Microsoft Corporation - WDDM v1.1), 256 Mb
Hard Drives: C: Total - 715394 MB, Free - 251750 MB; D: Total - 305234 MB, Free - 179084 MB;
Motherboard: Intel Corporation, DG43GT
Antivirus: Norton 360 Premier Edition, Updated and Enabled