Three times in the past week, my iPhone 3GS has died on me. The first time, it died while idle in my pocket. The second time, it died while idle in my pocket. This last time, it died while playing music in my pocket. Before it crapped itself, it made a static-like sound, like something short circuited. Each time it had about 40%-60% battery life. Was nowhere near flat. I thought it may have been an overheating issue since it was in my pocket while I was walking, but it felt quite cool to the touch after I took it out of its case.
The first time, I was able to restore it quite easily on my friend's computer. (I was at his house when it went.) It managed to turn itself on after being plugged in, so I went about my business and went home. By the time I got home, I found that it had gone off again. This time, it was a lot trickier to get into recovery mode. Eventually, four-and-a-half hours later/3 a.m., I got it into recovery mode and restored the whole thing. This latest bricking, almost a full week later, is giving me trouble again. I'm doing the whole 'hold the home button down while plugging in the cable' thing, but it's not working. Just stays on its dead blank screen. No Apple logo. No plug into iTunes icon. Just death. My iMac doesn't recognise it as being connected either.
Is there some method I'm missing? I've tried different power button/home button combos.


This latest bricking has convinced me to send it back to Apple and get it fixed/replaced/whatever they do. Until then, I still need a phone. 
It's never been jailbroken. The first two times, it was on 3.1.2. I updated this morning, so now it's on 3.1.3.


Sorry about the long winded post. I'm at the end of my tether right now. Seriously would consider smashing it if it didn't cost me my soul. Any advice besides sending it back or smashing it is welcome.