If you're switching to a desktop system from a laptop (I am assuming that's what you're calling the tower hard drive) you can get decent video cards with s-video out at reasonable prices. You can get a DVI to VGA adaptersc heap but I don't know of a DVI to s-video adapter.
Two options that I see based on the information you have given:
1) Get a video card that has an s-video port on it here is a range of PCI Express cards with s-video out. Here is a link with a list of cards that will do what you need. The cheapest one will do more than you need for just karaoke:
http://www.newegg.com/Product/ProductLi ... rchInDesc=
2) Get an expensive adapter that will step the DVI signal to S-video or composite.
Hope this helps!
<Edit> I said "sound card" when I meant video card. Sorry about that