Full scan does not scan everything.

A couple days ago my computer became infected and Norton I thought did a good job at taking care of it. But I notice whenever I try to click on a hyperlink from a search engine I get redirected to some bogus site that differs everytime. I have tried to perform a full system scan which usually takes at least an hour and it is finished within a minute or two and has only scanned 6,000 files but shows a completed scan. I know my computer is still infected but am at a loss on how to repair it. I have since installed spyware doctor which seemed to get rid of some things but the issues mentioned above are still present.