Ever heard of a product called DeoxIT? It's a contact cleaner spray that removes oxidation (tarnish) from electrical contacts. You may just have dirty contacts.
I always keep a can handy. It works VERY well. Good for cleaning scratchy or 'open' pots. Works great for cleaning Video-game cartridges and cartridge slots too! I've resurrected a few Genesis carts with it.
I'd spray some of that in the AV port and plug/unplug the connector a few times to work it into the contacting parts.
Now is a piece of plastic broken from the inside of the Av Out i think that i need a new Dreamcast....
If the AV port is busted, then you can always solder a SCART lead right to Dreamcast motherboard.