Your computer, no matter how old it is, has a connection known as a VGA connection. This analog format was what was once used to connect monitors to the computer and the cable usually is a beige or black cable with blue connectors at both ends. While this standard still exists today, those who have the ability to connect their computer digitally will choose to do so because of the reduction in latency and reliability of the digital connection.
Most TVs that were made after the year 2000 have a VGA port on them, especially if they were higher-end televisions. Every LCD or Plasma screen sold today has a VGA port, and so do almost 99% of all laptops, unless the laptop has an HDMI connection.
To connect the computer to the television this way, all you have to do is plug in this blue-tipped cable to both the television and the computer. If you don’t get an image on the screen, make sure Windows recognizes that you have an external display plugged in, and this is easiest to do on a PC that has a built in screen, like a laptop. Or, if your video card supports it, plug in two screens at once and troubleshoot that way.