Tech help: can anyone explain what's going on with my iPhone?

My iPhone makes no sound, except very rarely - why? 

I have an iPhone 3GS bought in June 2009 so it's pretty ancient and the battery rapidly discharges to zero when the phone is in use and says that it's at 80%. Probably I need a new one, but I'm clinging onto it until the absolute last possible moment.

A couple of months ago, while playing a piece of music, the speaker suddenly cut out and there was absolutely no more sound coming out. At first I wondered if the speaker had got wet and tried it a while later after presuming it had dried out - but it made no difference. I also tried cleaning out the headphone socket in case the sensor was confused and, thinking the headphone jack was present, blocked sound from being emitted from the speaker at the foot of the phone. No joy there either.

Because I use my phone as an alarm clock I realised that I'd have to use it on the vibrate setting, which I now do, although if I have headphones on while listening to music I can still hear the alarm or the phone ringing.

A few weeks later (thanks to my Twitter archive I can tell it was on 10 July 2013) my phone randomly began producing sound, which I noticed when my alarm clock both went off and vibrated. I was delighted that it had fixed itself I listened to a bit of music before it suddenly cut out again a while later.

Jump to 8 October (today) and it happened again this morning. I was woken by my alarm going off and vibrating away and noticed that I could also hear the alarm music coming from it too. Hooray. It let me play music for about 20 minutes (even with the volume at maximum I could barely hear it) before suddenly cutting out again.

Possibly it can only play 20 minutes of music very quietly every three months.

Can anyone explain what might be going on? Clearly it can play music, but it just doesn't.