I’m looking at an old Land Rover that has the basic transmission layout, Gearbox/transfer box in the center with prop shafts going to front and rear axles.
How can I check the front axle does actually work when in 4 wheel drive?
I imagine this would be outside someones house or on their driveway so test options would be limited.
You should be able to feel it binding when making turns.
If you can lay some sand or gravel ahead of the front wheels, I expect you could tell by the wheels kicking the sand/gravel back rather than just rolling through it. Note that on some (most? all?) systems that use front locking hubs, the front wheels have to roll a bit before the hubs engage. You may have to select 4WD, drive forward a bit to engage the hubs, and then lay the sand or gravel.
This. Lock the hubs put it in low range and try to make a tight turn.
If you have access to a piece of loose gravel or dirt, try pulling something immovable (another rig or perhaps even a tree) with a tow rope and see if at least one wheel on each axle is digging in. (If it has posi-trac, you will possibly see all four wheels digging.) If there is no gravel/dirt in the area, ask if you can use the seller’s front yard. 
If you’re going to drive/turn in 4WD on dry pavement to check for binding, please be gentle and back off at the first sign of resistance as this is one of the most common ways to break a 4WD.
Or… take it to a shop (which I would do anyway) for a quick once over.
If it has 4 low, put it in 4 low, first gear and drive straight. It will be super responsive to the accelerator input and will whine and tach out at like 10 mph. It will feel like you’re doing 60mph in first gear.
Yep. You should feel it not want to more forward. When it does, one tire will skip.
This will tell you if the low range in engaged, it will not tell you if the front axle is driving.
Ah yeah, good point, I guess a turn is the only foolproof way.
Thank you all for some good suggestions.
After posting I had the thought about jacking up one front wheel and trying to turn it.
If it is out of 4wd the wheel and prop shaft should spin freely but lock up if put into 4wd.
This would have to be done on both front wheels separately in case one of the half shafts is broken.
In an old “series” landrover (red lever for low/4WD, yellow for high 4WD), there is no central diff. So undo one end of the rear prop-shaft (4 bolts), engage 4WD and just see if you can creep a few centimetres. You could keep the handbrake on so you don’t move but you will feel the drive engage as you let ou the clutch.
On later models with a ful centre diff-lock, same procedure.
With the viscous diff-locks the complication is that non-movement could mean that the lock is not working. However these are permanent 4WD (as are some with manual locking diffs) so if the transfer box is so badly damaged I think you will know anyway:D
Note the handbrake works on all 4 wheels, so alternativelly, jack up the front and with the handbrake on, you and an assistant try to turn the wheels in the same direction.
This is an old Series 3 and from what I can remember from having owned one a lifetime ago there is no central differential and the handbrake works on the rear prop shaft.