Thanks - you ran the trouble shooter and checksur - neither solved the Windows Update (WU) issue
I understand - the hotfixes were from WU, I thought you might have run them independently. Speecy will show what WU has on your machine.
HP - gotta love 'em. I have a few myself.
You might try the standalone SP1
if you haven't already, and if that fails...
The repair install tutorial
explains how to create Windows install media that can be booted from a OD or USB. I don't like the name, but that's what MS references. I think older Windows simply refered to it as setup - not as ominous sounding as "install". Anyway, the repair is what's important.
Since you don't have SP1 installed Use option 6 6. Repair Installed Windows 7 without SP1 using Windows 7 without SP1 DVD/USB
I'm not certain if you could use option 4 or 5 (using the SP1 ISO or SP1 DVD/USB). That would be preferrable since it might not only fix the WU issue, but bring your machine up to SP1.
To be safe, go with option 6, and the associated "pain" of WU after SP1.