iPhone 3GS reboots and gets its display crazy

I've been facing this problem for the last 3-4 months. But the problem happens sporadically. When it happens I can't do anything else with the iPhone, even if I try to reset it. I just leave it alone and after 2-3 hours I try to turn it on again.

See the ENTIRE video of the problem happening. Falha iPhone - YouTube

I've already tried to reset it to default factory configuration but the problem happend even so. Which makes me believe it's not a software problem.

Any ideas about what could be the reason?

Just take it to an apple store, I took mine in when my home button started playing up and even without apple care they fixed it free of charge. It's worth a shot

I don't have an Apple Store in my city. I called Apple Support, but they told me that no matter what the problem is, I should pay around R$ 850,00 (about US$ 400.00) to have it fixed. I think they don't fix, they will give me a new one. That's why they want to charge me this amout of money.

Someone told me to download redsnow (which is for jailbreak, but it'd fix my problem), and select extras and then select the option to fix boot loop. I'm a little afraid of doing that.