Is there any way of checking whether I've got a battery or alternator problem?

I had to jump start my S1 last Sunday and I left it running for best part of an hour, I then took it for a 15 minute drive before letting it tick over for a further 30 minutes, as soon as I turned it off it wouldn't start again. There wasn't even enough power for the alarm to beep and the indicators to flash, and the remote locking/unlocking wouldn't work either.

So battery or alternator? Easiest way to find out?

Thanks in advance.

CheeRS