OK, I seem to have solved the problem. I moved ALL Dell folders to an external drive (I didn't want to just delete them of course) and then - without any Dell folders on my laptop - the installation finally completed successfully. Now the folders are back too after the installation. I had deleted everything recommended in threads, but apparently something else was interfering.
Hello, I had a problem yesterday checking drivers and running other tests because SupportAssist was not working properly, so I decided to uninstall and reinstall it (as an administrator of course), but installation fails every time, and I have done everything I have found in threads and in the video (deleting folders, entries in the registry etc.). I even tried in safe mode with networking, but it still failed. The BIOS is up-to-date too. I still have Dell Update in Control Panel (not mentioned in threads about SupportAssist installation failure). Should I uninstall it too? I have really done everything indicated in threads. Anything else I can do?  Thanks.    
SupportAssist won't install