I'd say it's a bit risky to add one of those into your controller, because if you got a warranty for it (IF YOU ONLY GOT IT A SHORT WHILE AGO that is) you have to hack into your controller to install the analog stick, and opening it up usually voids the warranty. Also, I've heard that the replacement analog sticks aren't exactly the best. Look in the video below https://www.youtube.com/watch?v=o3GYtAyR...

I have an Xbox 360 S but I've never had mine freeze before. However, I think I might have a solution to the Red Dot. I saw in a video that the red dot is caused because the console has a problem detecting the hard drive. The guy in that video said that "The Xbox was pushed a lot during transit and it won't work because of that" and you might have shaked or moved it to convey the same error. In the video, he took the hard drive out and put it back in again, and that seemed to do the trick. I hope that solved it! :)

The "Red Ring of Death" means something's wrong with the console. There are four types of Red-Ring errors you can get. Here are drawings of them: ^That means your console has an E74 error, or a type of error. It should usually display the type of error on your TV screen. ^That means your console is OVERHEATING. The inside is WAAAYYY too hot (usually happens if you play it too long) for the components to work and it needs some time to cool down. ^THAT is the infamous RROD. This is an issue that A LOT of Xbox 360 owners lost their 360 to. This can be caused by a variety of purposes. This was only an issue with the older models, because their voltage was too high. Microsoft came out with the Xenon model in 2005 and the Zephyr in 2007. These were 12V 16.5A, and they had a 54.2 percent failure rate. In late 2007, Microsoft rolled out the Opus and Falcon (the latter having HDMI) which were 12V 14.2A. This was better than before, but it still caused problems. In 2008 Microsoft released the Jasper, which is...

Your tv looks like it might have some broken pixels. I've seen TV's like that before, and that means that there's pixels there that aren't displaying correctly, thereby giving you that. It's usually caused by someone or something hitting it. Did someone there bump it? I lost a laptop because of pixel malfunction. I believe you MIGHT be able to get a screen replacement, but I can't guarantee there IS one for your specific TV. You could try, but I think it would be best to get a new TV :)