The whining could just be the bearings holding the props/VCU up - but if there were not serious problems, you would be very lucky.
First thing is to check that the prop you bought is OK. There are ways to do this with it off the car - but there isn't data of what results to check for - so you'll have to put it back on the car and do the "1 wheel up test" - I can explain it - but best to google it to find out what to do - basically a 1.2m bar on the hub nut and a 5kg weight to get a time of ideally 30 seconds, but no more than 60 or (maybe) 90. If you get that result then it is safe to put the prop on a car assuming the mechanicals you are bolting it to are OK.
You must ask yourself - why did the previous person remove the props? The answer is NOT (thats a BIG NOT) to improve fuel economy - that's rubbish. They removed them to hide a fault. It may be that the previous VCU was going 'tight' and the owner had the foresight to remove it before it damaged the transmission - very unlikely. It may be that the bearings holding the previous prop/VCU up were noisy - this is your best bet - but you are clutching at straws!
It is highly likely that the props were removed because the rear diff or, more likely, the IRD got trashed due to a mismatch of tyres, unevenly inflated tyres or an overly tight VCU.
If your new prop performs the 1 wheel up test OK - then probably the cheapest way to see if there is ant pre-existing damage to your diffs is to install it and see how it performs - you got a whinning - ws that the bearings on your new prop or something else? I say this is the cheapest way - its also the most dangerous - because if there is any pre-existing damage there is a possibility it can shatter your IRD and you can then no longer run even 2WD!
You can inspect the IRD for damage. Wiggle the rear pinion - there will be some rotary movement as gears mesh - but there should be no lateral movement (ie sideways). Change the oil in it and see what colour the old stuff comes out. If it comes out looking like 'oil' (you're looking for a dark brown colour that maybe might smell a bit) - then that's a sign the IRD is healthy. However, it may also show that there is a problem and the oil was changed when the problem occurred and it was changed to 2WD. When the oil is out, you can remove the rear pinion and chack for any damage to the teeth on the inside of it and the gear that it mates to. Any chipped or broken teeth and its basically not possible to reinstate 4WD. If all the checks so far are OK, then it is likely the IRD is OK - however - short of removing it, splitting it and examining all the bearings, there's no way to be absolutely sure.
I don't know so much about the rear diff - but the same principles will apply.
Good luck. It sounds like the Freelander isn't your biggest challenge, but hopefully its one you can enjoy
ps - what engine does it have?
