Hello RT999RT,
1. Did you make any changes to the system, prior to the issue?
Follow the link to check which updates are being installed.
http://windows.microsoft.com/en-US/windows7/See-which-Windows-updates-are-installed
Step 1:
You may configure the computer to clean boot state and then try to install the updates and check if that helps. To configure the computer to clean boot follow the link given below.
How to troubleshoot a problem by performing a clean boot in Windows Vista or in Windows 7:
http://support.microsoft.com/kb/929135
(Note: Follow step 7 from the link above to boot back in normal mode.)
Note: After you have finished troubleshooting, follow step 7 in the article to boot to normal startup.
Step 2:
Also you may download the stand alone packs for the updates and install them manually on your computer and check if that helps.
To download updates follow the link given below, put in the KB Article number to search for the update and then download and install the same.
http://www.microsoft.com/downloads/en/default.aspx
For the failed download and install the updates by checking the link mentioned above.
Step 3:
You may also try to run the fixit in the below given article
How do I reset Windows Update components?
http://support.microsoft.com/default.aspx/kb/971058
Also refer the link below for more information in the specified error code:
http://windows.microsoft.com/en-US/windows7/Windows-Update-error-1
Hope the information provided helps.