A quick look through the log doesn't show anything necessarily bad, though you have a lot of unecessary auto starts and therefore a lot of extra processes running all the time in the background. This can be a drain on system resources for sure. You also have what is called a questionable anti-spy program called Spywarebegone. This is not one of those usually recommended. I would uninstall that one.
You also are showing two, or at least portions of two anti-virus programs running, Avast and Symantec/Norton. This is definitely a no-no and can certainly cause lots of problems. Choose one and totally uninstall the other using Add/Remove, following any prompts you may be given like rebooting, and then also do a manual file search for any remainders.
You also are running Spybot TeaTimer, turn that portion of Spybot off. While Spybot is an excellent program the TeaTimer portion is really more trouble than it is worth. It runs all the time in the background and also can interfere with removal of some infections or malware. Keep the Spybot but turn off the TeaTimer. You can turn it off by going into the program itself and doing the following;
Go to Advanced Mode, Click Resident and take the checkmark out of Resident TeaTimer. Reboot the system.
I think you should begin by following the cleanup steps given on this sticky above Read me before posting a request for assistance
Then post back here with the requested logs along with information on the computer itself;
hard drive size and how much space is remaining, how much RAM is installed also.