I want to make a music video, for this I only need to do some cut-cut editing on the video, and be able to replace the original soundtrack with a soundtrack of my choice. What is the best program to do this? I can use Premiere but it's a bit too heavy-weight and my PC gets pretty slow when I use it, making it difficult to do some very precise editing. And I'm not going to use half of its functions.

Did you try Pinnacle Studio or Vegas Movie Studio?

Just for grins try MovieMaker 2 (free with service pack 2). On your original soundtrack, simply mute the volume, Make your cuts, fades, etc, then drag your new sound file onto the timeline and render.

I don't know if the available output modes will work for your needs though. However, the price is right