I'm not at all familiar with "Spysweeper," but suspect that a program which is designed to protect your privacy by preventing, [I assume] people from knowing what you're doing on the web, may be overprotecting you and erasing all your traces...including all bookmarks and cookies [small numeric tags installed as you visit sites interacting with other programs, etc.] You're likely "not signed into Google" because it's helpfully wiped the cookie that Google would use to identify your machine. Personally, I just use Norton Internet and not even all of it, because most of these programs have real problems telling friend from foe. I'd suggest that you disable SpySweeper for a while---if it's got a disable option---and see if that fixes your problem. Just stay off suspect sites while your guard is down: don't gamble, don't answer spam ads, and don't go to porn or marginal entertainment sites, don't let any other user do so, and you'll generally be much safer: these sites are notoriously full of hitchhikers. If you can't get it to disconnect, try going to Control Panel and go through the Add/Remove Programs procedures to boot the thing off your computer.
BUT: back up all data before beginning to do battle with this program. I don't trust it, after hearing what it's doing, and be safe: be sure you have a copy of everything you care about before trying to pry this thing off your disk. Five will get you ten it leaves some crap in the registry, but it may play nice and just get off your computer until you [for some reason] reinstall it.
If on the other hand removing it doesn't reset your defaults in Internet Options to don't-erase, go into Internet Options as I've indicated above and look at what the settings are: if it is set to erase things, set it not to erase, and that should fix that, while getting it off your disk should fix its interference in your browsing.
Understand: all the above is based on my personal belief that this program is the root of your problem, and I am NOT a computer expert. If these steps are too foreign to you, review them with someone who knows that area of Control Panel and is familiar with uninstalling programs and walk through this proposed action with a second opinion.