If your computer is an older computer and it has any viruses or malware on the computer then that could cause a potential slow down of your internet speed through the computer.
But just having an old computer should not cause any problems with your internet speed.
I have a 10 year old desktop computer that I upgraded from windows xp to windows 10 and I don't notice an decrease in my internet speed.
Your CPU and ram could be slowing down your computer but not the internet speed.