A/V jack messed up- Screen flickers on and off

The first place to start would be the cable itself, it might have a kink in it therefore causing the bad connection. If you hold it in a certain position does the picture and audio come back? That would probably be the simplest way to fix it, but not permanent. Then move on to the connector itself, does it feel more loose than normal? if so, then its most likely a bad soldier joint. One more thing to consider is the contact pins might be bent out of alignment but thats probably not the case. iFixit sells Wii motherboards, but they're a bit pricy. See if you can find a Wii on Ebay for parts, and unsolder the AV connector form the bad one and put it in yours.

Good luck.