Billy, I don't understand your last question?
Computer speed is determined by the operation to be performed and speed of the individual components involved. There is a big difference between playing a game and a disk intensive program for instance. Another would be writing a letter/document. Three different processes that would act differently.
Game - depends on genre, action or fairly static, let's say a first person shooter, car race, or hidden object game. Let us just consider non-internet versions too. The first two would more depend on the video aspects of the game, that would determine the level of detail and the speed of the action. A good example of this is MS's Flight Simulator. It outputs the video, called frame rate based on the detail an options you enable. Don't have enough video memory and select a lot of options (video detail) and the frame rate slows down. Part of that equation is the processor and how fast it can create the needed image as well. Go below 20 or so frames per second and the output will appear jerky. Not a good experience.
'Stable' display games like Hidden Object games might not put a load on your system, in that the display will show the detail that it can, set by the resolution you choose. Since the scene hardly changes, other than a removal of an item and some word changes, even the slowest computer can handle this easily. Only performance related item based on CPU and disk speed would be going between scenes.
Internet speed, well it varies all over the place. Some or actually most of it, out of your control. What you can control is the speed you purchase, depends on your ISP and even how much traffic is on the ISP's line you are on. Individual network cards AND drivers can effect overall speed too. Almost all h/w in desktops that are hard wired is fast enough to handle any speed an ISP gives you. Wireless, another story. Depending on Protocol used (speed, N or G), distance from the Router, quality of the router and its firmware, and any possible signal interference (portable phones, microwaves, etc.), and distance from the router, you can drop below the speed delivered by the ISP.
Do you have a specific question?