You have a consistant drain on the battery somewhere...

First thing to do would be to get the car started somehow, probably jumping it off another car and then with a multimeter measure the battery voltage. It should be up around 14.4v ish whilst the engine is running. If it isn't, then your alternator isn't charging it.
The alternator runs the electrics whilst the engine is running, not the battery. So, another test you can do in the dark is to drive up to a wall parking as close as you can to it with the bonnet. Then with your headlights on, rev the engine. You should see your headlights against the wall get slightly brighter. If they don't, again you've got an alternator issue.

If all that checks out ok, then you will need to go into the passenger compartment fuse box with everything switched off and with a multimeter check all the fuses to see what current is flowing through them. Typically, you should no higher drain on any circuit than about 15-20mA. If you have a circuit which is pulling a lot larger than this amount then this is where your drain is and you will need to find out what electrical systems are run on that fuse circuit and then check them all out individually.

However - My gut feeling is you have a charging problem. The reason I say that is because you say your dash lights went dimmer when you put the headlights on with the engine running. This indicates to me that the battery is running the electrics when the engine is running not the alternator. Again the fact that you can go for a drive and then the battery is completely dead signals this. Because the ECU/injectors etc all need electricity to operate, if you have a charged battery and then go for a drive without the battery being charged on route and the alternator not working, it will soon run out of juice.

Check that alternator out again and let us know how you get on.

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"Supercharged - 454.1bhp/317.5lb/ft"
Peugeot 306 GTi-6
2000 (X), Moonstone

Yes, as the existing battery cable goes from the battery terminal to the rear of the starter, and then from there links straight to the alternator.

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"Supercharged - 454.1bhp/317.5lb/ft"
Peugeot 306 GTi-6
2000 (X), Moonstone

Any updates on this Mick?

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"Supercharged - 454.1bhp/317.5lb/ft"
Peugeot 306 GTi-6
2000 (X), Moonstone

Yep, broken connection somewhere mate.

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"Supercharged - 454.1bhp/317.5lb/ft"
Peugeot 306 GTi-6
2000 (X), Moonstone

I am away from home at the moment, but I will have a look at the wiring when I get back to my car this weekend and let you know where I believe the fault will most likely be.

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"Supercharged - 454.1bhp/317.5lb/ft"
Peugeot 306 GTi-6
2000 (X), Moonstone

I have had a look and there doesn't seem to be much wiring, it's fairly simple....

Are you sure the alternator has been tested and is working correctly?

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"Supercharged - 454.1bhp/317.5lb/ft"
Peugeot 306 GTi-6
2000 (X), Moonstone

Sounds like a bad earth to me ?

Check the 2 earths on the gear box and the earths under the battery box

Keep us updated mate, this could make an interesting FAQ when you manage to find the issue.

It has to be a bad/corroded connection or earth connection as Chris says if the alternators have been confirmed as working.

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"Supercharged - 454.1bhp/317.5lb/ft"
Peugeot 306 GTi-6
2000 (X), Moonstone