You've gotten a lot of good answers, so I'm going to do some out of the box thinking - maybe it will spark a few ideas.
Goal:
self hosted server on boat
Issues:
size
power
corrosion
So if I were going to do this myself, I'd start with a pelican or other similar watertight container. We don't want the equipment getting wet, and we don't want it exposed to the salty air.
I'd probably pick a usff computer, like a dell 9020 or maybe a framework motherboard. To get the storage, I'd get one of these to add multiple sata ports to the computer. Then its a matter of getting a bunch of ssds and powering them. I think the 12v goal is going to be too restrictive, most laptops need 19v to charge, so I'd just bite the bullet and get an inverter. If you're really tight on power you could go with a pi, but the framework motherboard/usff both use mobile processors, and shouldn't draw too much while idle.
Any wires that pass though to the case should be made through waterproof bulkheads.
Personally I'd nix the HDMI out requirement. One more port to keep track of and it complicates the self hosting. If you want it for media streaming to a TV then I'd recommend a roku and just run a jellyfin server on the computer. If you want it for server debugging I wouldn't bother running it out of the case.
The last thing I'd do is figure out cooling. For this I'd probably create some sort of closed loop heat exchanger from the case to either the outside air or the lake/ocean itself. This could be as simple as a pump running water through two radiators, one in the case and the other outside or just dumped overboard. If you know your power usage ahead of time you might be able to get away with a peltier element, dumping the heat outside the case.
I'd probably put this all on its own power system, get a solar panel, battery, inverter, etc. It could even get topped off by the boat's system if it needs extra juice.
Also whatever you do, I'd figure out a way to ensure you're giving your system a clean and steady 12v.