SD reader is detected by the system? Try to Update the Windows if yes. If that doesn't help UNINSTALL reader drivers (all) and then try update again. If above didn't help make sure you have correct drivers. Best to do that is to look on HP driver site for your system.
If still have problems try to Run the Hardware troubleshooter and check:
press Windows key + C on your keyboard for the Charms bar,
type Troubleshooting and then click Troubleshooting under Settings,
now type Hardware Troubleshooter in the search option,
Click on Hardware troubleshooter to run the troubleshooter.
If that doesn't work try following:
http://support.microsoft.com/kb/929833
http://windows.microsoft.com/en-in/windows-8/windows-update-error-0x800f081f