>>invent a new type of rotation resistant power and video cable
That should not be difficult, plug cables into the base instead of directly into the screen and have circular donut shaped plates connecting the base and the screen instead of cables. The plates do of course have to have a spring to put the correct pressure to give a good connection even after some wear on the plates
Instead of mechanical slip-rings use fiber-optic rotary joint so you avoid awkward bandwidth limitations. You could probably make do with plain off-the-shelf components here
That should not be difficult, plug cables into the base instead of directly into the screen and have circular donut shaped plates connecting the base and the screen instead of cables. The plates do of course have to have a spring to put the correct pressure to give a good connection even after some wear on the plates