There are a few things to consider here.
For ease, a good baseline to follow is 10# for every gallon of water and decoration. Your tank will need to have additional framework that can support the outward action on the glass/plexi. DO NOT count on the PC case to be structurally rigid enough for that. Traditional tank frame would be a sturdy rectangle (or shape of tank) on top and bottom.
It is easy enough to build your own custom tank based on the dimensions you have available. You can use any food grade silicone sealant to caulk in your edges and "glue " it all together. For plexi there are various glues that can be utilized. I STILL recommend using silicone on those as well. I would suggest building the tank, allowing it to dry completely and then test fill the tank before it is even inside the house. Keep in mind the weight I specify above. Fresh water weighs about 8# a gallon. It is typically recommended to have AT LEAST 1# of substrate (gravel) for each gallon and often times works out better going more.
I say that aspect to consider your placement. I already mention that it needs a sturdy frame from blowing apart, but also needs a stable base that will not warp/bend/go out of level over time with that weight on it.
Small fishtanks (less volume of water) are harder to keep in that they are more reactive to temperature, pH changes, and things of that nature. Recommended bioload on an established fish tank is typically benchmarked at 1" of fish per gallon of water.
You need to consider filtration, lighting, heat or possibly even cooling.
In my own couple of seconds thinking about this, I would likely go with a completely custom made tank/case/stand. I would build the tank with a spillway system and have all the filtration and water care, fill level and such done from the sump tank down below. Personally think I would concentrate on a clear tank ~10-15 gallons on the front side and framed in such that the motherboard is stacked up behind the tank. Probably utilize some strategic LED lighting strips, perhaps some LED RAM on the motherboard and behind such as to provide lighting along with a bit of "play" in the reflections.
The last aspect is that all fish tanks get mineral creep around the areas that evaporating water escapes, like around the lid, up the heater cord, such as that. This is going to be an extremely humid environment almost regardless of what you do. This situation would be compounded by the heat generated (as mentioned above) an the air flow needed for the components.
As to cooling, it would be super duper cool if you could figure out a way to incorporate a water block using fish tank water. I would be concerned about possible (specifically) copper leaching into the water. Once that gets high enough it will cause invertebrates to dissolve and shortly after that will kill fish.
I think it's a darned neat idea, particularly as a project for short term. I would consider the long term care and keeping operable PC parts in that proximity to the humidity and such would quickly grow tiresome.