The base for this build is a LCD-386 Portable Computer, which I found on ebay kleinanzeigen and just had to have. Took it apart, cleaned over 20 years worth of dust and got to work.
Now it is home to a capable gaming machine featuring modern parts like a Ryzen 5 5600X, 16GB of ram and a RTX 3070 GPU.
Watercooling was mandatory in this case, because there wouldn't be any room for a decent sized air cooled gpu + I wanted to keep the apperance as close to the original as possible. So no more holes for airflow then necessary.
For the GPU I had to go with a Founders Edition design, because of the limited depth. I tried fitting two different cards beforehand, but they were too tall.
The original display was removed and replaced with a 11.6 inch, 1440p portable IPS display. The power is wired to a molex connector, which runs off the internal PSU and the display signal is handled by a flat HDMI cable going to the GPU.
Unfortunately it doesn't quite fit the original bezel, so I have to run at 2304×1440 pixels, with small black bars on top and bottom. It is possible to game on it, Nvidias control panel can force any game into that resolution, but I would prefer to use it as a second monitor.
I intended to keep the original keyboard, but had only problems using 5 pin DIN adapters. Instead, I replaced the whole thing with a Coolermaster Quickfire TK and coiled the cable around some bamboo stick we had. Fortunately, this keyboard's form factor is near identical to the original keyboard, so I only needed to do a couple small cuts on the chassis and was able to put it in place. Some 3D printed brackets hold it in place.