Fatal error: core update wordpress 4.2.1

your theme “ninezeroseven” seems to be the issue.

To rule out any theme specific issue, try switching to the unedited default Twenty Fifteen theme for a moment using the WP dashboard to rule out any theme-specific issue (theme functions can interfere like plugins). If you don’t have access to your admin area, use FTP or whatever file management application your host provides. Navigate to /wp-content/themes/ and switch to the default theme by renaming your current theme’s folder by adding “-old” to the end of the folder name. Alternately, you can remove other themes except the default theme. That will force your site to use it.

– If that does not resolve the issue, also try resetting the plugins folder by FTP. Sometimes, an apparently inactive plugin can still cause problems. Also remember to deactivate any plugins in the mu-plugins folder (if you have created such folder). The easiest way is to rename that folder to mu-plugins-old.