For some reason, when i touch my two leads on ground and then on 5V, I get random quick little beeps.
Your multimeter sends out a small voltage to do continuity. When you touch one lead on 5v, and the other on ground, you are sending a small voltage through the CPU, regulators, resistors, diodes, capacitors, and the GPU before it gets back to your other lead. It is very, very bad to send foreign voltages through any solid state component, and can fry your Game Cube (or whatever else you are working on).
I was carefully testing continuity on my board when I accidentally touched the wrong lead. When I turned my GC on, there was interference on the screen and my controller didn't work. I had to let it sit overnight before it started working again.
Moral of the story, DON'T EVER USE CONTINUITY ON COMPLEX MOTHERBOARDS.
I just don't want you to fry your mobo.