Check for updates hanging in Win 7 has been a common complaint of late and the problem may be on MS's end.
Some have found that having their update settings set to auto and let them come themselves has been the easiest solution, whereas I've seen someone post that prior to running the Check for updates was to go to Installed Updates first and then they didn't have to wait so long before it found them.
Did you run the Pre-Scan in Step 2 to see if there were any errors reported with any of the files ?
If those services aren't starting however, then you could have other problems.
Run the program again in Safe Mode to see if you get the same report.
If you do then go Start - type cmd - right click on cmd and select Run as administrator - accept the UAC and enter sfc /scannow
If that reports it is unable to repair some files, then run SFCFix.exe which will produce a more concise report which you can copy & paste.
https://www.sysnative.com/niemiro/apps/SFCFix.exeIf the sfc /scannow reports no violations then go Start - type services.msc and press enter.
Scroll down to Background Intelligent Services - click on it and then on Start in the upper left pane to see if it will start then go onto do the same for Windows Module Installer.
The default setting for those two should show as Manual.
The Windows Update service should be showing as Started and Automatic (Delayed) although you can click on it then on Restart in the upper left pane.
Let us know if you have any problems with those.
