How to fix Windows 7 stuck on 'Checking for Updates'

Manually download and install the following patches.
I recommended to disconnect your PC from the internet and do a restart before you install these.

1. Service Pack 1, if you don't have it already
2. Install root cert update
3. Install client update
4. Perform the normal Windows update

If you still have issues after that, then try WSUS Offline to download and apply the updates.

For a walkthrough tutorial and more information, see this video.