First up, I know this is General Hardware, and the title might indicate a software problem. However, the circumstances of this failure feel more like there's a hardware issue at play. Mods: if you feel this is better suited elsewhere, please feel free to move it and accept my apologies. 
The PC in question isn't mine, and is pretty long in the tooth. It has a Pentium IV processor (~3 GHz), 3x 1GB DDR2 RAM sticks. Not sure of the GPU. It was running Windows 10 upgraded from Windows 8. There was a notification to install the Anniversary update, and that's when the problem started. The update failed, and Windows attempted to roll back. This in turn seems to have failed, and now it's stuck in a boot loop where it tries to complete the update, fails, tries to roll back but immediately reboots.
Because it's in the middle of an update, there's no way of getting into safe mode. I made a Win 10 recovery USB image, and the PC will boot from it but it sits there for a while with the Windows logo, then reboots (i.e. it won't get into the recovery menu). We've tried the same thing with a DVD, and the same thing happens.
I've run memtest86 which passes with no errors. I've also run a few CPU tests (such as mersenne) and they also pass. The fact that the PC won't boot up the Windows recovery utility gives me the impression that it's falling over when trying to load a driver but there's no output so no clue what it might be. We've made sure everything extraneous is unplugged (other than mouse and keyboard) but no luck.
So I'm looking for further advice on how we might go about diagnosing what's wrong and potentially getting the PC back into a working state for the short term.
Thanks!

The PC in question isn't mine, and is pretty long in the tooth. It has a Pentium IV processor (~3 GHz), 3x 1GB DDR2 RAM sticks. Not sure of the GPU. It was running Windows 10 upgraded from Windows 8. There was a notification to install the Anniversary update, and that's when the problem started. The update failed, and Windows attempted to roll back. This in turn seems to have failed, and now it's stuck in a boot loop where it tries to complete the update, fails, tries to roll back but immediately reboots.
Because it's in the middle of an update, there's no way of getting into safe mode. I made a Win 10 recovery USB image, and the PC will boot from it but it sits there for a while with the Windows logo, then reboots (i.e. it won't get into the recovery menu). We've tried the same thing with a DVD, and the same thing happens.
I've run memtest86 which passes with no errors. I've also run a few CPU tests (such as mersenne) and they also pass. The fact that the PC won't boot up the Windows recovery utility gives me the impression that it's falling over when trying to load a driver but there's no output so no clue what it might be. We've made sure everything extraneous is unplugged (other than mouse and keyboard) but no luck.
So I'm looking for further advice on how we might go about diagnosing what's wrong and potentially getting the PC back into a working state for the short term.
Thanks!