Are there any software / hardware tests that one should perform if this happens?
Note No, I haven't actually done so. I just need to know about this issue beforehand should it happen in future.
Most components are very light and can therefore withstand the mechanical stress of a fall quite well. CPUs mounted with big cooling systems are more at risk. Their connectors may break, bend or loosen, causing the component to fail entirely. For criticial hardware, this is easily diagnosed. For random access memory, network cards and so on, quickly checking whether your OS can still detect their presence will suffice.
The keyboard ought to be able to take a serious beating, but it's worth doing a simple test to confirm all keystrokes are still registered and none of the keys are stuck.
Notebook displays are generally delicate too, but if it goes on and does not show any pixel faults, it has probably not been significantly damaged.
The number one thing to look out for is the mechanical hard drive. Not only is this component the most likely one to be broken in a fall, its damage may not be immediately apparent. You'll probably want to check it thouroughly. If supported, as is the case with most modern hard drives, the SMART data can provide valuable information on the health of the device and it is recommended to follow up with a scan for bad sectors.
In short, check the following:
The biggest issues from a drop to the floor are:
You did not note any abnormalities while powered, but if you have a hard drive you would want to review it's SMART info to see if there has been any damage to the drive with something like Hdtune.