What about after safe boot and deleting all the cache your browsers and mail create?
And try cloning and test the clone.
6GB RAM should be 'okay' for basics but all depends what you are requiring it to do.
I am running Safari in 10.6.8 on a 2009 MacPro 2.93 four-core.
Safai is using at most 0.4 percent of the CPU. At the moment, I have 5 tabs open. BUT -- I am using "Click-to-Flash" or rather its follow-on ClicktoPlugin to suppress the automatic playing of Flash Videos.