I would personally lay the bet on it being the battery. Its a classic sign, and to be fair, even a battery 24 hours old can be flat, if there is a drain on the electrical system, it makes no odds as to when it was new
When you got the new battery, did you get a calcium silver? Normal lead-acid is no good for the Mondeo's so-called "smart charge" system.
The other thing is, have you got one of these silly amplifiers in the boot? If that isn't wired up correctly it could be putting a permanent drain on the battery - it's meant to go off when the ignition is off.
 Did you actually see the filings in the old starter? If they really were there, then that's a classic symptom of a failing DMF. If you didn't, is there a possibility that the garage was trying to railroad you into paying for a DMF you don't actually need?
could be faulty alternator, could be just a duff battery, its hard to diagnose, unless you have a multimeter and the ability to do a reading?
with the engine running, if you put the battery across the positive and negative battery terminals, you should be getting around 14v.
you'll most likely have ground fault or parasitic-drain somewhere,(or somethings on that shouldnt be).
If the battery doesnt cure it,& its got enough current flowing etc,your best bet might be to get a good auto sparky to have a look.electric problems like this can be really difficult to find unless you know exactly what youre doin & can read diagram/schematics like the back o your hand.
sorry i thought you had a new alternator. i'd say duff alternator. I have a new alternator sitting here,thats only done 500miles. i got it then wanted to do freewheel pulley modification,but didnt wanna chance pulley not fitting so bought another one off ebay & fitted pulley,then fitted it to car.worked great so left it on.hence having a new spare. let me know if you want a good deal
ps: an alternator (refurbed) will cost you £100. brand new visteon:£240 odd if i remember correctly.
You can pick up a secondhand alternator for £20 and a new one for £79.99
And the aux belt for £12.20
of course the aux belt only drives the alternator and air con, the power steering and the waterpump are driven from a different belt
Put the battery off my dads car on it and it fired up straight away. So now gotta work out what drained it. On the day of the problems i had drove the car about 25 miles,parked up at the supermarket,in there for about 15 mins,went back to the car and dials went round and it struggled to start. Drove it round to my moms about 5 mins away and parked it up,tried to start it again and it was dead. Managed to bump start it,drove it home about 25 miles away,tried it again outside my house as soon as id parked up and turned ignition off and nothing,completely dead. Didn't even attempt to start. any ideas anyone? Thanks
Just in case it hasn't become clear, it sounds like your problem is not that (mystery) drain is flattening your battery, but that the battery isn't charging.
Now, there can be a couple of reasons for this; the alternator is shot, or there is a wiring problem with a relatively high resistance causing charging to be at a very low current. I only mention the second because it is much cheaper and simpler to fix if that is the problem; an alternator problem is statistically more likely, but more difficult/expensive to fix.
(BTW, it sounds like you have a spare battery, currently - keep that charged. It also sounds like the previous owner had the 'battery flat' problem, and replaced the battery, even though the battery itself wasn't the primary problem. Also, after all of the messing around with the battery, it ought to be possible to dismiss the idea that there is corrosion on the battery terminals, but maybe not).
Anyway, depending on temperature, etc, the voltage on a battery with everything off ought to be about 12 volts, with the engine running and no big loads on, slightly more, and with the engine revving at, say 2000 rpm, about 14.4 volts. My guess is that you won't see the voltage go up much as you rev the engine, and maybe all of the voltages will be low. The other test is to put some big loads on (heated windows, heater fan, lights), and with 2000 rpm you should still have a decent voltage. If the voltage drops off under load under 12 volts, partic if the drive belt screams a bit, then maybe the drive belt is slack/greasy.
Probably alternator, but maybe wiring or drive belt.