Sorry for taking so long. It took me a while to back everything up. This is the result of the diagnostic test that you asked me to run. I did the test when my access to websites was already lost:
Start time: 15:52:38 08/03/14
Model Identifier: iMac11,1
System Version: OS X 10.9.4 (13E28)
Kernel Version: Darwin 13.3.0
Boot Mode: Normal
Time since boot: 17:53
Admin access: No
SATA
WDC WD1001FALS-40U9B0
FileVault: FileVault master keychain appears to be installed
Diagnostic reports
2014-07-05 PerianUpdateChecker crash
2014-07-05 PerianUpdateChecker crash
2014-07-05 PerianUpdateChecker crash
2014-07-05 PerianUpdateChecker crash
2014-07-05 PerianUpdateChecker crash
2014-07-20 PerianUpdateChecker crash
2014-07-21 PerianUpdateChecker crash
2014-07-21 PerianUpdateChecker crash
2014-07-22 PerianUpdateChecker crash
2014-07-24 PerianUpdateChecker crash
2014-07-24 PerianUpdateChecker crash
2014-07-26 steam crash
kexts
com.sophos.nke.swi (9.0.53)
com.sophos.kext.sav (9.0.61)
Agents
org.macosforge.xquartz.startx
com.sophos.uiserver
com.google.keystone.system.agent
com.valvesoftware.steamclean
com.adobe.ARM.UUID
launchd
/Library/LaunchAgents/com.google.keystone.agent.plist
- com.google.keystone.system.agent
/Library/LaunchAgents/com.sophos.uiserver.plist
- com.sophos.uiserver
/Library/LaunchAgents/org.macosforge.xquartz.startx.plist
- org.macosforge.xquartz.startx
/Library/LaunchDaemons/com.adobe.fpsaud.plist
- com.adobe.fpsaud
/Library/LaunchDaemons/com.google.keystone.daemon.plist
- com.google.keystone.daemon
/Library/LaunchDaemons/com.sibelius.sari.plist
- com.sibelius.sari
/Library/LaunchDaemons/com.sibelius.sibelius6.plist
- com.sibelius.sibelius6
/Library/LaunchDaemons/com.sophos.autoupdate.plist
- com.sophos.autoupdate
/Library/LaunchDaemons/com.sophos.configuration.plist
- com.sophos.configuration
/Library/LaunchDaemons/com.sophos.intercheck.plist
- com.sophos.intercheck
/Library/LaunchDaemons/com.sophos.notification.plist
- com.sophos.notification
/Library/LaunchDaemons/com.sophos.scan.plist
- com.sophos.scan
/Library/LaunchDaemons/com.sophos.sxld.plist
- com.sophos.sxld
/Library/LaunchDaemons/com.sophos.webd.plist
- com.sophos.webd
/Library/LaunchDaemons/org.macosforge.xquartz.privileged_startx.plist
- org.macosforge.xquartz.privileged_startx
Library/LaunchAgents/com.adobe.ARM.UUID.plist
- com.adobe.ARM.UUID
Library/LaunchAgents/com.valvesoftware.steamclean.plist
- com.valvesoftware.steamclean
Startup items
/Library/StartupItems/KodakDatabase/daemon
/Library/StartupItems/KodakDatabase/KodakDatabase
/Library/StartupItems/KodakDatabase/libwrapper.jnilib
/Library/StartupItems/KodakDatabase/StartupParameters.plist
/Library/StartupItems/KodakDatabase/wrapper
/Library/StartupItems/KodakWebPortal/daemon
/Library/StartupItems/KodakWebPortal/KodakWebPortal
/Library/StartupItems/KodakWebPortal/libwrapper.jnilib
/Library/StartupItems/KodakWebPortal/StartupParameters.plist
/Library/StartupItems/KodakWebPortal/wrapper
Bundles
/System/Library/Extensions/SophosNetworkInterceptor.kext
- com.sophos.nke.swi
/System/Library/Extensions/SophosOnAccessInterceptor.kext
- com.sophos.kext.sav
/Library/Audio/MIDI Drivers/EmagicUSBMIDIDriver.plugin
- info.emagic.driver.unitor
/Library/Audio/Plug-Ins/Components/GM_Module_AU.component
- com.m-audio.rigs.gm.sib
/Library/Extensions/SophosNetworkInterceptor.kext
- com.sophos.nke.swi
/Library/Extensions/SophosOnAccessInterceptor.kext
- com.sophos.kext.sav
/Library/Internet Plug-Ins/AdobePDFViewer.plugin
- com.adobe.acrobat.pdfviewer
/Library/Internet Plug-Ins/AdobePDFViewerNPAPI.plugin
- com.adobe.acrobat.pdfviewerNPAPI
/Library/Internet Plug-Ins/DivXBrowserPlugin.plugin
- com.divx.DivXBrowserPlugin
/Library/Internet Plug-Ins/Flash Player.plugin
- N/A
/Library/Internet Plug-Ins/Flip4Mac WMV Plugin.plugin
- net.telestream.wmv.plugin
/Library/Internet Plug-Ins/Flip4Mac WMV Plugin.webplugin
- net.telestream.wmv.webplugin
/Library/Internet Plug-Ins/Google Earth Web Plug-in.plugin
- com.Google.GoogleEarthPlugin.plugin
/Library/Internet Plug-Ins/googletalkbrowserplugin.plugin
- com.google.googletalkbrowserplugin
/Library/Internet Plug-Ins/iPhotoPhotocast.plugin
- com.apple.plugin.iPhotoPhotocast
/Library/Internet Plug-Ins/o1dbrowserplugin.plugin
- com.google.o1dbrowserplugin
/Library/Internet Plug-Ins/OfficeLiveBrowserPlugin.plugin
- com.microsoft.officelive.browserplugin
/Library/Internet Plug-Ins/OVSHelper.plugin
- com.divx.OVSHelper
/Library/Internet Plug-Ins/Scorch.plugin
- com.sibelius.scorch
/Library/Internet Plug-Ins/Silverlight.plugin
- com.microsoft.SilverlightPlugin
/Library/Internet Plug-Ins/Unity Web Player.plugin
- com.unity.UnityWebPlayer
/Library/Internet Plug-Ins (Disabled)/Flash Player.plugin
- N/A
/Library/PreferencePanes/DivX.prefPane
- com.divx.divxprefs
/Library/PreferencePanes/Flash Player.prefPane
- com.adobe.flashplayerpreferences
/Library/PreferencePanes/Flip4Mac WMV.prefPane
- net.telestream.wmv.prefpane
/Library/Spotlight/GBSpotlightImporter.mdimporter
- com.apple.garageband.spotlightimporter
Library/Audio/Plug-Ins/Components/A52Codec.component
- com.shepmater.A52Codec
Library/Caches/com.apple.Safari/Extensions/DivXHTML5.safairextension
- com.divx.DivXHTML5
Library/Caches/com.apple.Safari/Extensions/Searchme-2.safariextension
- com.spigot.safari.searchme
Library/Internet Plug-Ins/Picasa.plugin
- com.google.PicasaPlugin
Library/Internet Plug-Ins/SOEWebInstaller.plugin
- com.sony.soe.WebInstallerPlugin
Library/PreferencePanes/Perian.prefPane
- org.perian.PerianPane
Library/QuickTime/AC3MovieImport.component
- com.cod3r.ac3movieimport
Library/QuickTime/Perian.component
- org.perian.Perian
Contents of /etc/ssh_config
Host *
XAuthLocation /opt/X11/bin/xauth
Contents of /etc/sshd_config
SyslogFacility AUTHPRIV
AuthorizedKeysFile .ssh/authorized_keys
UsePrivilegeSeparation sandbox # Default for new installations.
AcceptEnv LANG LC_*
Subsystem sftp /usr/libexec/sftp-server
XAuthLocation /opt/X11/bin/xauth
Contents of /System/Library/LaunchDaemons/com.apple.screensharing.plist (XML document text)
<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
<plist version="1.0">
<dict>
<key>Disabled</key>
<false/>
<key>EnableTransactions</key>
<true/>
<key>GroupName</key>
<string>wheel</string>
<key>Label</key>
<string>com.apple.screensharing</string>
<key>MachServices</key>
<dict>
<key>com.apple.screensharing.server</key>
<dict>
<key>HideUntilCheckIn</key>
<true/>
<key>ResetAtClose</key>
<true/>
</dict>
</dict>
<key>ProgramArguments</key>
<array>
<string>/System/Library/CoreServices/RemoteManagement/screensharingd.bundle/Con tents/MacOS/screensharingd</string>
...and 17 more line(s)
Font issues: 40
Firewall: On
Parental Controls: On
Safari extensions
DivX Plus Web Player HTML5 <video>
Searchme
Restricted files: 21355
Elapsed time (s): 164