I suggest you try step-by-step instructions in m#l's thread Updates not working, it has been searching for updates for hours and then post back if you have any problems.
The instructions require you to manually pre-install any of the five Win32K.sys listed on Dalai's webpage at http://wu.krelay.de/en/ if one or more are missing from your system. That list currently includes KB3161664 (MS16-073: Description of the security update for kernel mode drivers: June 14, 2016). Once all five of those Win32K.sys updates are installed your Windows Update should run normally (i.e., "Checking for updates..." should finish in ~ 20 min) and install any pending updates, including your remaining June 2016 Patch Tuesday updates. From Dalai's webpage at http://wu.krelay.de/en/:
"This HowTo is valid for Win7 SP1 and Vista SP2, which have been newly installed or haven't been updated for some time. It should also help on systems that were up-to-date last month - just install the missing updates from the list below...
...The term "solution" might be a little bit exaggerated, since the following HowTo only tries to make sure that the Update Agent doesn't need to check all updates, so the check for new updates is done faster. Futhermore, it's only a temporary solution; most likely the issue will appear again with the next Patchday."
32-bit Vista Home Premium SP2 * Firefox v47.0 * NIS v126.96.36.199 * MBAM Premium v2.2.1
HP Pavilion dv6835ca, Intel Core2Duo T5550 @ 1.83 GHz, 3 GB RAM, NVIDIA GeForce 8400M GS
Edited by lmacri, 28 June 2016 - 10:33 PM.