Whenever I start up Windows, LW starts up as well. Whenever I try to close it down, it starts back up about a minute later. No matter how many times I close the program down, it always starts itself up. I tried uninstalling and re-installing it again, but the same thing kept happening.

Well it's obvious you haven't read the Sticky at the top of this section which has all your answers. I wont say anymore but to say you have a virus & here's a direct link: LimeWire continually Popping up every few seconds & also Opening at System Startup