May I suggest that AVG is a terrible antivirus, and causes many problems in the windows environment, including messing with internet connections? I've witnessed this first hand multiple times. It could be a part of your problem. In order to remove it (if you take my advice), you will need to install its removal tool, since antiviruses are not easily removed. This is the link to the software called AVG remover: AVG - Download tools and utilities
Here is a well known, clean, light, and strong antivirus if you are interested in it instead: Microsoft Security Essentials - Free Antivirus for Windows
I do not know much about zone alarm, but I do know windows. I recommend using the windows firewall over any other firewall (and never installing 3rd party firewalls), but again it is your choice.
You will not need windows defender if an antivirus is installed, as it automatically is disabled when you upgrade to having an antivirus (Defender becomes obsolete).
I also can help you get your computer up to speed if you would prefer not to do a clean install, but if you would rather clean install, let me know and I can link you to a good tutorial on how to do it near perfectly.
If you would like to save your programs, I am not sure how you would do it other than creating an image: Backup Complete Computer - Create an Image Backup
...But then I am sure the speeds wouldn't get better if you used it with all that you have now. There is a better option of saving files and music to a USB drive and just loading them on a new clean install, but other than those 2 options, I wouldn't know a third. The second option will limit just what you can save by what you can load onto the USB drive, however, and may not be what you want. Let me know if any of this sounds good.