The most likely cause of your slowdown and connectivity issues is a lack of maintenance. Do you ever run antivirus and antispyware scans? Do you clean out your old files to make sure you have some spare room on your harddrive? Do you run programs to clean out your Registry and optimize system settings? Assuming that you run Windows XP, follow the steps in this guide to start cleaning up your machine. This will help you get back to that "new machine" feel.
Keep in mind that a system is only capable of running so much without getting sluggish. If your machine feels slow, you could be demading a lot more out of it than you used to. The type of programs you decide to run in the background can take up a lot of processor time and memory. What programs do you run to play your music and do your downloads?
Since you multitask, having sufficient RAM is crucial. The bare minimum amount of RAM most people should have now is 512MB and at least 1GB is recommended. So, if you are looking for a starting point to tweak your system, start with your RAM.
You have a 40GB harddrive and say that you are low on space? What does low mean to you? 5GB free? 1GB free? 100MB free? 0MB free? You say that you wouldn't buy a new harddrive unless you bought a new machine. Why is that? You can get harddrives very innexpensively. You can get 80GB of additional storage for less than $60. That would effectively triple the amount of storage space you have on your machine. You can put all your music and other media files on the additional storage so you wouldn't lose it if you had to format your drive and reinstall Windows. The benefits of having a secondary drive are numerous and the cost is low.
As for your processor, since you say that you don't run processor-heavy games, you should be fine with 2GHz for a while. Keep in mind though that minimum specs to run programs refers to running just that program, not that program in addition to ten other things in the background. I really have no idea why that Football game (that doesn't even have you actually play Football) would require so many resources. It sounds like a bit of a resource hog to me.