Find Out What is Wrong in the First Place
It's all well and good for all of us who have never looked at your computer say to try this or switch to that. There can be MANY issues that will slow down your computer. I do a performance study of mine or one from work when someone tells me it was slow. Here are some things I have found:
1) Memory - as someone already pointed out, a lot of application programmers assume that you have a modern (less than a month old) computer when designing and coding their apps. Regardless of the "minimum" requirements on the package or user guide, they usually are talking about minimum resources just to run the software and not to run it well. Think of the software you had on your computer when it ran great. Now, what has changed or has been "upgraded".
2) Processor - see discussion on processor, above.
3) Hard Disk - This has its roots in several places. First of all, older hard drives are, well, slow. Remember that the technology that the drive uses must match your disk controller if you want to buy something newer. Then there is the issue of transfer rate. How fast can the data get from the drive into your memory? Latency and other issues can slow you down. Another thing to watch out for is disk errors. With age, more errors show up even though the hardware corrects for these and even moves your data around, there still would be a slowing effect. Some people swear by the speed of Solid State Disk (SSD) drives. Fine but I have seen some weird things happen with these that indicate space is not freed up exactly when files are deleted (older SSD) and there is still information out there that they have limited lifespans with regard to read/write cycles. Defragging? It may help. Has little to do anymore with the physical drive characteristics but it still is a factor in the use of "clusters" by Microsoft's NTFS. (Stll, I would not suggest running this on an SSD). Checkdisk (or CHKDSK)! Very important, especially if you have something messed up in part of your NTFS system.
4. Software - As someone pointed out, the less junk you have around, the cleaner and better your system should run. Think about this: if you have an anti-virus program and it does a scan, which computer would it run faster on? One that is near empty in terms of number and size of files or one that has a kazillion files and many are large? What would I do? Go to the control panel and get rid of anything that a) you know what it is and b) you don't need it. What about LINUX? If you have time to learn something new, this could be great. If you don't have the time or patience, this could be frustrating. Always try it before you buy it!
5) Startup - If the computer is slow starting up, try to figure out what is running at start up. Have a techie show you how to work MSCONFIG.EXE. You can use it to stop all programs from starting up when your computer starts (careful not to stop normal Windows stuff). If it runs better, you can go into there and allow more and more to start up until you find out where the slowdown is.
6) Task Manager - If the slowdown is during normal running, you can run the task manager (right click on taskbar and then select task manager from the menu). If you go to the processes and sort by the CPU column, things that seem to be taking up a LOT of CPU (except "idle") could be worth looking up and seeing what they relate to.
7) Malware - You've seen that malware doesn't always have the slowing effect but it could have. There are many free anti-virus programs out there but, you really could need more. Not all malware programs are viruses. Adware, spyware are things that you not only want to get rid of but can slow you down as well. I don't trust an A?V program to get rid of these very well. Try a free download of Spybot Search and Destroy. You don't need to run "Tea Timer" in the background, just update it, do an immunization and a scan every once in awhile, especially if things seem slow or just plain weird. Too much scanning? That could be an issue, especially with most anti-malware software that scans. Here's what they do: Your computer starts. The malware software immediately starts (so you're not unprotected during startup), then the software decides that it needs to check for updates (all this while your PC is still trying to start) and, after downloading updates, it might start doing a scan. Should you go into settings and tone it down? You can, but the more you tone down your anti-malware software, the less safe you are. The question then becomes, are you TOO safe? Is it worth "some" risk to speed up your PC? Maybe. It depends on your environment and what you do with the PC. Spend a lot of time going to weird sites or sites that have a lot of advertising that they show from elsewhere? or do you just run Word mostly?
My suggestion is to find someone local to you who works as a technician on computers every day and someone you trus and offer to take them to dinner if they can do a thorough study of your PC. You will need to show them where it is slow for you and what you do with the PC. The last PC I looked at that was "slow" was trying to connect with a server in China often.