Hiya. Work through these steps to Clean Up Factory Bloatware
which can smother Windows 7 on low resource machines. Especially establish a Clean Boot to get all of the freeloaders out of startup.
I see you're running the most problematic AV we see here, MucAfee. I would uninstall it and install in it's place free Microsoft Security Essentials.
Once you've worked through all of these steps here are other Troubleshooting Steps for Windows 7
which will familarize you with the logs, system resources, hardware tests, and other steps to become the master of your PC.
Finally we have in residence here the top expert on tracing slow startups and shutdowns who will help you if necessary with Gathering a Startup, Shutdown, Sleep, Hibernate, or Reboot Trace - Windows 7 Forums.
But try everything else first.