Lucy

If you receive Windows Update error 80070003 while checking for updates, you need to remove the temporary files that Windows uses to identify updates for your computer. To remove the temporary files, stop the Windows Update service, delete the temporary update files, restart the Windows Update service, and then try to check for Windows updates again.
The windows Update Troubleshooter is available that fixes some problems with Windows Update, and it might resolve this error for you. 
 
If that didn't work, try the following steps.
 
To stop the Windows Update service
You must be logged on as an administrator to perform these steps.
1.      Open Administrative Tools by clicking the Start button, and then clicking Control Panel. In the search box, type administrative tools, and then click Administrative Tools.
2.      Double-click Services. If you're prompted for an administrator password or confirmation, type the password or provide confirmation.
3.      Click the Name column heading to sort the names in reverse order. Find the Windows Update service, right-click it, and then click Stop.
 
To delete temporary update files
1.      Open Computer by clicking the Start button, and then clicking Computer.
2.      Double-click the local hard disk where Windows is installed (typically, drive C).
3.      Double-click the Windows folder, and then double-click the SoftwareDistribution folder.
4.      Double-click the DataStore folder to open it, and then delete all files in the folder. If you're prompted for an administrator password or confirmation, type the password or provide confirmation.
5.      Click the Back button. In the SoftwareDistribution folder, double-click the Download folder to open it, delete all files in the folder, and then close the window. If you're prompted for an administrator password or confirmation, type the password or provide confirmation.
 
To restart the Windows Update service
You must be logged on as an administrator to perform these steps.
1.      Open Administrative Tools by clicking the Start button , and then clicking Control Panel. In the search box, type administrative tools, and then click Administrative Tools.
2.      Double-click Services. If you're prompted for an administrator password or confirmation, type the password or provide confirmation.
3.      Click the Name column heading to sort the names in reverse order. Find the Windows Update service, right-click it, and then click Start.
4.      Close the Services window and the Administrative Tools window.