Norton has a free scanner without their product or logging in.
Best PC Protection - Computer Security Tools - Norton
Can't give a direct link because it's a popup box. But to the right, under Resources, second on the list is a free scan, and it'll also analyze how vulnerable it thinks your computer is. (Of course, in the long run, they want you to buy their products, but it might give you some useful info.)
Don't know how this compares to some other stuff, but about 3 years ago when I got a backdoor trojan and then got attacked by everything else before I knew what was going on, this thing found a bunch of stuff that the installed AV didn't. And it also had instructions for removal and occasionally a free removal tool.
Once you hopefully get this taken care of, get an AV running all the time, plus spyware. (I personally use Avast and Spybot. I don't actually like Norton but the online thing worked pretty well.)