Well, this sounds really familiar...
I know you don't have a whole lot of aftermarket stuff, but in my case it was the relay on my stereo amps that wouldn't kick off in the colder weather. I also just happened to help my buddy with the '06 Mark LT, his turned out to be the relay on the gauge cluster.
Amp draw test is your only way really find out. It is easy once you get it set up.
the below is stolen...
The current (Amps) is what you need to be measuring. The value will change instantly depending on how much power is being drawn from the battery.
***** Note: Whilst the multimeter is connected following the instructions below, DO NOT turn the ignition switch on or turn any high power items on (such as the headlights),The leads of a multimeter are not large enough to handle this amount of power. As the car appears to be drawing a very large current (based on the time it takes your battery to go flat), I would even go as far as to suggest you at least pull out any fuse rated 10A and above (and preferably all the fuses) and all relays before connecting the multimeter, then measure the current changes as you put them back in.
To measure the current (Amps) being drawn from the battery:
Disconnect the battery negative terminal (disconnecting and using the positive terminal for testing as you indicated in your original post is not advised as an accidental slip with the battery cable or multimeter leads could ground the wiring, causing blown fuses/electronics or at worst a fire).
Set your multimeter to read Amps. If your multimeter can read AC or DC Amps then you need to use DC Amps. Use the largest Amp scale the multimeter will accept (typically 10A on a small DIY multimeter, this is the bare minimum you will probably need). Some multimeters will require you to plug the red lead into a different socket when you are reading Amps, please check first.
Note: If the current drain of your car is as high as I suspect it is, this next step may cause the multimeter to go off the scale, blow a fuse or heat up it's wires. Be ready to disconnect it.
Connect the negative lead of the multimeter to the negative battery terminal. Connect the other lead of the multimeter to the ground lead you removed from the battery.
You should now have a reading in Amps indicating the current drain. If you pulled all the fuses and relays before beginning the test it should be reading below 0.1A and probably zero. If the value is still high then I would first suspect the ignition switch is not disconnecting the power correctly when you turn the ignition off (based on your observation that the dash computer has remained on with the key removed).
You should now be able to remove/replace fuses and relays and disconnect components until you locate the culprit. You may see very small fluctuations in the readings but this is normal. What you are looking for is a larger change, say 0.2A and above. Good luck and let us know how you get on.
As a rough guide, a 12 watt trunk bulb will draw approx 1 Amp, a 60 watt head light bulb 5 Amps (Watts divided by 12(volts) = Amps)
Batteries have a power rating printed on them.
A 70Ah (Amp hour) battery, for example, is rated to provide 1 Amp for 70 hours (at approximately 12 volts for the whole time). If the current drain is 2 Amps then it will provide 12v for half the time (35 hours) and at 3 amps it will provide 12v for a third of the time (23.3 hours). If your car is draining the battery in two hours then there is a very large current drain (somewhere in the region of 35 Amps depending on the battery rating), larger than most fuses can handle.
When the car is turned off and depending on the equipment installed in the car which is permanantly on (e.g. alarm, immobiliser) you should be aiming for a current drain of less than 0.1A (4 weeks using a 70Ah battery).