Dont be silly.
While a true engineer can do anything with duct-tape, it is best to reach for the proper materials. In this case, you want
indexed metal strapping tape, a drill gun, and some lag-bolts with washers and nuts, and at least 1/8 inch thick metal plate (for both sides of the door).
Some contact adhesive cement for initial setup is good too, as it will help you drill the needed thru-holes in the door.
You will need at least 4 bolts, 12 washers, and 8 nuts. (yes, 2 nuts per bolt. Trust me.)
Form then cut the strapping tape, so that follows the countour of the computer case, and extends away flush with the bottom of the case enough for at least one hole with a washer at each end.
Use the contact adhesive to stick the 1/8 inch plate to the inside and outside of the doorframe. This is very important, as modern "wood" interior doors are very flimsy inside, and have no mechanical supporting value. Once stuck, use the measured and cut strapping as a drill jig (oriented vertically!), to drill the thru-holes through both sides of the door (and plating). Affix the strapping at the bottom (only!) and secure tightly. Slide the computer case in through the sides, and position to your preference, then affix the top.
When affixing, you should use 1 washer on the front side, with the fixed head of the through bolt-- then 2 washers, and 2 nuts per bolt on the back side. Tighten each nut separately; One nut on each of the four corners, until good and snug, then the next 4 nuts after that, tightened as tight as you can make them, to prevent the first nut from moving after the fact. (this mechanically puts a bind on the first nut on each of the bolts, and thus prevents them from turning due to the jostling of the door being opened and shut.)
The bolts might stick out a bit on the other side of the door. For safety reasons, you should use a cutting disk to cut them down with just a small amount exiting the locking nut, then bevel the cut edge to avoid nasty cuts and scrapes.
For maximum durability of the door's hinge, you should put this nearest to the hinge mechanism as is feasible.
(this is of course, not something you should EVER do-- but, if you are intent on doing it, the above is the proper way to do it.