Try the step-by-step instructions on page 1 of m#l's thread Updates not working, it has been searching for updates for hours in the MS Answers forum. Those instructions have been revised for December 2016 and will be valid until the January 2017 Patch Tuesday updates are released on 10-Jan-2016.
Depending on the last time Windows Update ran to completion on your sister's computer, you might find that all six of the Windows kernel-mode driver (Win32K.sys) speed up patches listed in STEP # 2 are missing and have to be manually installed. And "speed up" is a relative term - if her system is missing 10 months of updates I would be prepared to leave the manual Windows Update (STEP # 6) running overnight to see if "Checking for updates..." eventually runs to completion.
32-bit Vista Home Premium SP2 * Firefox v50.0.1 * NIS v188.8.131.52 * MBAM Premium v2.2.1