This may or may not be possible. If it is a mechanical spin drive almost assured that it could be used as an external. However, if an SSD, it is likely just chips mounted on the motherboard and cannot be removed to use as an external. It is sort of a 50/50 thing as to if an SSD is soldered to the motherboard or in a socket. If in a socket, no issue.
@GaryE : Did you try removing all power, including the battery, and hitting the power button a few times to discharge all the capacitors and then restore power? Sometimes this is easier said than done. For instance both my Mac-book air and Microsoft Surface have batteries that would need the case opened to disconnect the battery. What removing all power does is a true reset of the system as when plugged in or with the battery the thing is never truly off.
From how you described the failure I doubt that the hard drive is actually dead so the advice from
@Alice B is totally valid to check out as, if the drive is removable, you can recover the file you were working on at the time.
Has this system ever been dropped, especially if recently? Again this depends on if there are sockets for the memory that can be accessed through a panel on the bottom or if it is hardwired. If accessible through a bottom panel make sure the memory (RAM) cards are properly set in place. Easiest way to make sure the cards are set properly is to remove and seat again. I remember getting so mad at a client when I had my computer business as she denied the laptop ever being dropped yet I could see the dent in the corner from the drop. Opened the bottom panel for the memory and sure enough the drop had knocked loose both memory cards. Re-seated and the system was fine. LOL! I really wondered about some clients as they wanted me to fix the system but would lie as to what happened. When it came to viruses and malware I know some of the lies were due to embarrassment as tracing the infection would lead to a porn site as the cause but, still, if you want someone to fix something correctly you have to be honest. I mean, if you called a plumber to fix a leak in your kitchen, would you tell them the problem was in the bathroom??? Sorry for the 'mini-rant' but some clients REALLY ticked me off and your issue brought back memories. I don't, in ANY way, to imply that you are not totally honest as to your issue; just brought back memories.