A slow computer can make it seem like the internet connection is slow but it's not the slow computer causing the slow internet connection.
Sometimes your web browser might stop responding or take awhile for the page to load up into the web browser but that is usually a fault of your slow computer and not having enough RAM or memory to allow the web browser to load properly.
Sometimes installing some more ram in your computer can be enough to help speed up your computer or cleaning out old unused programs and files and shutting things down that don't need to be running in the background.
Also if anyone else in your house gets on the internet it can cause your internet service to slow down as well or when other people in the neighborhood get onto the internet and start downloading files and streaming music, videos etc then that creates a bottleneck on the internet lines and creates a traffic jam.
That then causes your internet connection to slow down.