To do that TS will have to go purchase a special adapter that will connect it to the IDE or SATA connection to access it. It is a 2.5" HDD...not a 3.5" HDD. ( 2.5HDD are usually used for notebook computers.)
But if the TS has a spare 2.5" HDD lying about to test if the casing unit is working perfectly, they can take the spare 2.5'HDD and install it in the externat drive casing after removing the suspected faulty 2.5"HDD to see if he can access the spare HDD now.
If he can't access the spare 2.5" HDD..then it is the casing that has problems possibly not the 2.5" HDD. That at least narrow it down further. If you can read the spare 2.5" HDD then
your original 2.5" HDD is most likely damaged.
Usually if something is wrong with the external casing, it is the circuit board or something but I have yet to hear of any shop that does repair for them as they are too cheap to justify repairing. Your HDD on the other hand usually comes with a warranty and you should be able to sent it to a shop to repair it but of course you know the warranty covers trying to repair the hardward....your personal data on it are not.