Without a model number I can't see if that model had WIFI and without the number of meters or feet I can't say wifi is the answer. But let's note that AC POWERLINE BRIDGES are an option for many.
Google or use Amazon to find AC POWERLINE BRIDGES. As the maker documents what these are, how to use and install I'll stop here.
My home system consists of a desktop which is connected to a router by cable, and a laptop which connects wirelessly. I'd like to move my desktop to another room which is far from my modem and router. Is it true that one computer has to be connected by wire? I'm not even sure that my desktop has wireless capability. Desktop is a 2 yr old HP Pavilion and uses Windows Vista if that matters.