Video output distorted and broken fan pins

my PS2 fat series is SCPH-39006. The video output is distorted although audio output is fine. Im planning to fix it myself as i do have quite a handful of soldering experience and i know the basics of hardware stuff and i do have all the equipments to do so. so i thought this would be a good experience. But once i open it i realized i have no idea what im doing and in the process of opening it and trying to get the fan off it appears to broke off. My question is

1. Where do i start looking or begin with trying to fix the video issues?
2. Can i just solder back the fan? It will be a pain to remove later but if it works then it works. But if someone have another idea that would be great
3. Here are pictures of the motherboard

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Picture of broken fan pin thingy (my english isnt great)