iWant a Healthy iPhone

Has my iPhone reached it's final days?? I charge it fully every night and unless I use up lots of talk time (rare) or listen to lots of music (also rare these days), it's usually still pretty full when I plug it in the following night. BUT yesterday evening I went to check the time and it didn't light up. I pressed and held the home button... then pressed and held the off button... then I pressed and held BOTH buttons, but nothing. I plugged it into the charger attempting to illicit some kind of response, and after a good minute, the dead battery sign came up.

Wtf?? It was dead? Weird, I thought... but could have been a fluke, I guess. So I let it charge back up and unplugged it again. Just 4 hours later, it was dead again. I've never had an issue with battery life before! But now I can't keep it on for longer than a few hours, and it's really warm! This will not do.

I got it as a Christmas gift in 2007, so I guess it's kinda old, but I would think it should still operate. It's a first generation 8 gigabyte iPhone, and it's been unlocked and jailbroken, so I really don't think that Apple would do anything for me.

It NEEDS to survive. It would be the loss of not only my phone, but also my iPod! Paul thinks that he can simply open it up and replace the battery... but I'm skeptical. I don't want to end up with a pile of parts.

Anny ideas??