The first line of defense is to make sure the computer's operating system (OS) has the current updates. Check Microsoft Security and Critical Updates or Apple's Software Updates. Next is a good antivirus program and an additional anti-malware program, both of which will be close to worthless unless you are (or it is automatically) downloading and installing the latest virus definition files and running scheduled scans. Java Adobe Flash and Reader should also be current. These three programs, when not updated, frequently lead to an infected computer. Unfortunately, being tricked into using a fake Adobe Flash update is the most common way of getting malware installed on any computer. (Read this article on Malware.)
Now that the OS and all software is up to date, the next consideration is a firewall. There are three kinds, packet filters (NAT,) stateful inspection (SPI) and proxys. Large companies use all three and they can cost thousands of dollars. Most of the routers we buy today for home and office use include both NAT & SPI and both are turned on by default. Further protection is available with a Virtual Private Network (VPN) which can be installed on both computers and mobile devices at a cost of $70 to $160 a year.
If you are using only the gateway router provided by your ISP, it may not have both NAT and SPI, and if it does, there is the possibility that one or the other (or both) are turned off. This occurs because these units are passed from customer to customer and are rarely inspected by cable companies or their customers. Asking a cable tech to show you that they are working and at what level is always a good idea. And if you are so inclined, you can do it yourself with a Google search or a call to your ISP.
If you suspect a virus or other invasive program, you can scan your system online or with retail antivirus software. The web links listed in Online Help could be helpful in determining the problem or in confirming your system is clean, if you are in doubt. Please follow the manufacturers directions. Please note that not all malware can be reliably removed from an infected computer with just one application, particularly with multiple infections involving rootkits.