A while ago my laptop decided that it wasn't going to download and install Windows Updates in the background any more. I tried to open the Windows Updates window and all it said was that the service could not be started. I decided to dig around on the web and was unsurprised at the number of "Try stopping it and starting it again" suggestions, as well as "Switch off your anti-virus", all of which were useless.
A little more digging led me to the right way to fix it...
First Things First...
First of all, run the Disk Cleanup tool (Accessories | System Tools | Disk Cleanup). If it gives you the option to clean up old system files as well, do that too. This will eliminate as much garbage on your drive(s) as possible, which you'll want if there are any partially-downloaded or corrupt packages downloaded.
The second thing to do is to download and run the Windows Update Troubleshooter (https://support.microsoft.com/en-us/help/4027322/windows-update-troubleshooter). This warns that it may take "a few minutes" but it took around half an hour on my machine. At the end of the run you'll get a list of problems it managed to fix, and others that it failed to correct.
Use your favourite search engine to look up the errors that the troubleshooter couldn't fix. This may be a pain but your system is already in better shape than it was when you started, so you're heading in the right direction.
The errors I got were:
Service Registration is missing or corrupt, windows update error 0x80070490
This allowed me to mess around with the System File Checker from an admin command line - take a look at the Technet Forum https://social.technet.microsoft.com/Forums/en-US/b0337275-fc86-40c0-b9e4-863d79eaea79/service-registration-is-missing-or-corrupt-windows-update-error-0x8007049020171202t082750p?forum=w7itproperf for full details of how to fix this.
Windows Update Error 0x8024402c
This was a strange one, and is caused by networking settings in Internet Explorer, which I haven't used in ages. There's a description of how to fix this at: https://www.drivereasy.com/knowledge/fix-windows-update-error-0x8024402c-solved/
Once I'd fixed the two errors that the Windows Update Troubleshooter couldn't handle, I retarted my laptop (mostly out of habit) and it spent the rest of the evening downloading all of the latest patches from MS.
If you're having similar problems with Windows 7 refusing to update, I'd recommend starting there. I'm not saying it'll work for you (don't even think of blaming me if it all goes horribly wrong) but it worked for me, and let's face it if your computer isn't updating Windows you're going to have some serious security problems eventually.