The typical home PC can be "hacked" or "hijacked" for various reasons, but the intention is usually malicious and profit based. Hacking is accomplished with various types of malware that run scripts that take control of the underlying code of the operating system to discover sensitive information about the user or otherwise inconvenience him. A number of red flags are present for users to watch out for so they can take corrective actions.
Many sophisticated hacking scripts and malware programs overflow your computer's memory and central processing unit (CPU) usage, slowing down your computer dramatically. To prevent more technically savvy users from discovering the processes that control this malicious code, some malware actually disables use of the Task Manager on Windows PCs.
One immediate telltale sign of malware is that your default browser's homepage has changed to something strange, usually something involving music downloads, porn or some other product. Malware almost always disallows the user from changing this site and usually uses this code to bombard the user with incessant pop-ups and pop-unders.
One insidious "genre" of malware is the false warning, which poses as an antivirus scan or malware warning, complete with tooltip pop-ups in the task bar, realistic looking "virus scanning" and scary sounding verbiage. The idea is to get unsuspecting users to click through to buy the antivirus software, which is just a scheme to obtain credit card information.
Some malware actually changes your network settings to use DNS and proxy servers that reroute your Internet traffic through unscrupulous providers who are mining your system for information, which you'd unwittingly be volunteering. As with many malware types, malicious codes may actually prevent you from changing these settings to something appropriate.