If your computer seems like it running very slow it comes down to a few different problems. The first thing to suspect is a virus, malware, spyware or adware. These are the most common things that will sneak in. What you need to do is download and install free malwarebytes, spybot and junk removal tool as well as rogue killer. Update and scan with each in the safe mode with networking. If you find a good amount of infections I would suggest taking the computer to a professional computer service center and have it properly cleaned.
The next problem that can cause slowness is a defective piece of hardware . It could be due to a failing hard drive with bad sectors or bad clusters. If you tackle this problem you will need to run check disk from a administrator command prompt. You will need to run chkdsk /r and this will scan the hard drive and correct the problems. Next you should shut the computer off immediately after check disk and then connect a new hard drive and run a cloning program. Once the cloning is done install the new hard drive in the laptop or desktop. Once again if you are not comfortable with this take your computer to a professional computer service center.
The last two possible problems may be a hard drive that is almost full. In this case follow the cloning method to a newer larger hard drive. The next possible problem could be defective memory. You can run free memtest86+ and test the memory. Replace any memory that is found to fail. Also make sure there isn't any dust built up in the heatsink, fans and case. It is possible that there are bad leaking expanding capacitors or a failing power supply.
As I have said earlier take the computer to a professional computer service center.