Limewire keeps starting back up almost as soon as i shut it down & keeps slowing down my system.
How can I stop that from happening?

There are two possible reasons I can think of that happening, the 2nd is the most likely & is the ugly reason.

1. Go to LW's menu bar, Tools > Options > System Tray / Shutdown & choose Shutdown immediately & press apply.

2. You may have a common gnutella virus. See WARNING: Viruses on network you should be aware of! (click on blue link). The better & easier solutions are the latter ones added in black text in part 2.

For some unknown reason the problem stopped as soon as I installed BitDefender.
I didn't do anything but installed it and the problem stopped.