Why is their only sound but no picture with my Wii?  (AV HDMI converter) sound but no picture  just a blue screen with the words "No Signal"?

video port broken, Take it to a professional repair place.

Either your cord or your HDMI adapter is bad.

The AV to HDMI converter has a yellow, white, and red input that i connect of all three by color with the Wii AV cable cord

Does your converter have a yellow input or red/green/blue input?

And are you using the same cable for the Wii with the same colors?

--- EDIT ---

Have you tried other devices with the converter?  If they don't work then the converter itself could be the problem.

Have you tried the cable with other devices to check if the cable is the problem?

It's probably one of those two but without testing them on other devices we won't be able to know which one is the issue.