Don't buy a used computer.
This can be very situational and I don't mean this as a hard rule.
Buying used hardware comes with many unknowns. You have no idea what problems will creep up. Saving a little money in this way does not pay off in the long run. You are far better off buying a new machine. Not only will it be faster, it will come with a warrenty.
I can help you transfer all your files from your old compuer to a new one even if your old computer no longer works.
Fixing an older computer vs buying a new one.
As a general rule if the computer is 3-4 years old replacement is the best option.
There comes a time when it's best to just replace your older computer when something serious goes wrong. Yes, it will cost more at the time but you will save money over the long run. Not only that, but you will have a much faster computer when you are done. If your current computer is over three years old then even the cheapest computer of the shelf is going to be ten times faster right out of the box.
I am happy to help you select a new computer from any major brand, or if you prefer I can build you a custom computer specific to your needs.
Use Google Chrome or Firefox.
Google Chrome and Firefox provide a much safer and faster internet experience than Internet Explorer. I strongly suggest that you install one of these browsers and use it daily.