|The problem is, you tried to delete it using Windows add/remove programs. |
You needed to use the (Start - Applications - ESET - ESET Uninstaller.)
Since you have started you will now have to use the uninstall tool, which may fail?
If it fails try Start-Search-All Files and Folders. type in Eset Nod32 antivirus in the search bar. When done click on the files found and delete them. Restart your pc and try downloading your new AV program.
If this still doesn't work you will have unhide hidden files and folders and delete it manually. Try the above first and see how it goes.