Bad luck
I don't know exactly where to look. But a general principle for gadgets and machinery is that the moving parts are the most likely to have trouble. The Gemini's moving part is the hinge, and what surrounds it. In particular, there are almost certainly ribbon cable(s) carrying power and signals to/from the keyboard, ports, &c -- cables which flex every time the Gemini is opened or closed. Those seem the most likely sources of trouble.
(I'm also drawing on years of experience with Psions: hinge mechanisms and the connectors around them were always the weak points.)
First thing I'd suggest is to contact Planet; it seems they can be quite generous when it comes to troubled units.
Otherwise, I'd try removing the top panel, bottom panel, and hinge panel, and try to make sure the ribbon(s) have their ends firmly seated, &c.
And I hope you get it sorted!