To speed your computer up, upgrade!
Though computer hardware is a key factor for the speed of computer but there are some other factors also which contribute to slowing down of computer. Main things that slow down are the programs and other stuff you have on the computer. When your computer starts, many things get loaded into memory and each one of those takes that little bit more of the computers resources. When you switch to a new program and don't remove the old one, the older one will still use resources.