Strange problem i've never encountered before. I think we'll need more information on your setup in order to correct this problem. Good job describing thr problem, just not enough info on your individual Xbox setup. I.E. cables used, version of xbox, mod chip, bios version, dash version, bla bla bla.....
Is your xbox mod chipped?
Did this problem just happen, or after modding something
May sound stupid, but did you inspect the AV connector for any flaws/bent pins? Did you try moving/wiggleing the cable around to see if it has a broken/shorted wire?