I hope that's the free trial and that you didn't pay for it. A combination of AdAwareSE, Spybot S&D and SpywareBlaster on a system, all of which are free, will protect you just as much if not more than spysweeper.
If you can' access the net without turning it off, it seems like it might be using some form of real-time protection. If you can, try disabling that, and see if the program becomes stable again. If not, uninstall it and re-install it on a clean boot, making sure there are as few background processes running as possible when installing.