http websites will not load

You might see if this article helps: If Safari doesn't load a page or webpage items are missing. What sort of update did you install?

If you have not already done so, try the following:

Run OS Recovery

Disconnect all devices from your computer except for the keyboard & mouse.

Boot up from your computer by holding down the command+r keys. This will take you to the recovery drive.

Select Disk Utility & hit Return.

In Disk Utility select the HD on the left & click on Repair Disk (bottom right).

When you reach the desktop after doing the above, again repair permissions & restart your computer.

Try reinstalling the security update. Are you sure the update was for Mountain Lion Safari? Also, try this:

Repair the Hard Drive and Permissions - Yosemite, Mavericks, Mountain Lion or Lion

Boot to the Recovery HD:

Restart the computer and after the chime press and hold down the COMMAND and R keys until the menu screen appears. Alternatively, restart the computer and after the chime press and hold down the OPTION key until the boot manager screen appears. Select the Recovery HD and click on the downward pointing arrow button.

Repair

When the recovery menu appears select Disk Utility and press the Continue button. After Disk Utility loads select the Macintosh HD entry from the the left side list. Click on the First Aid tab, then click on the Repair Disk button. If Disk Utility reports any errors that have been fixed, then re-run Repair Disk until no errors are reported. If no errors are reported click on the Repair Permissions button. Wait until the operation completes, then quit Disk Utility and return to the main menu. Select Restart from the Apple menu.

I hope you understand that a security update will not change the OS X version, so if that's what you are looking for, then know that the version number does not change for a security update.

Try a restart.

Do a backup, using either Time Machine or a cloning program, to ensure files/data can be recovered. Two backups are better than one.

Try setting up another admin user account to see if the same problem continues. If Back-to-My Mac is selected in System Preferences, the Guest account will not work. The intent is to see if it is specific to one account or a system wide problem. This account can be deleted later.

Isolating an issue by using another user account

If the problem is still there, try booting into the Safe Mode using your normal account. Disconnect all peripherals except those needed for the test. Shut down the computer and then power it back up after waiting 10 seconds. Immediately after hearing the startup chime, hold down the shift key and continue to hold it until the gray Apple icon and a progress bar appear. The boot up is significantly slower than normal. This will reset some caches, forces a directory check, and disables all startup and login items, among other things. When you reboot normally, the initial reboot may be slower than normal. If the system operates normally, there may be 3rd party applications which are causing a problem. Try deleting/disabling the third party applications after a restart by using the application un-installer. For each disable/delete, you will need to restart if you don't do them all at once.

Safe Mode

Isolating an issue by using another user account - Apple Support

Great find! Added to my KB Article listing.

😁