Depending upon your version type of PCB ).?? Below is an image of D10 on a Gemini 1 ver 2 pcb and ver 1 PCB..
Version 1 and some version 2's have diode D10 (dual common anode, in a SOT23-3 package), which is prone to "blowing" (usually caused by someone doing something, but they do run close to their tolerance) which will cut 5V to HC and many other Gemini ICs (depends upon how it "blows").??? You mentioned you have CR2032 thus there is a possibility you have one of these Gemini's.??? Later version Gemini 2s and ver 3 Gemini 1s didn't have this diode and instead had D10/D11, typical SMA diodes.
As Paul stated, Fuse F2 is the most common cause of the HC going blank see attached image.? Usually its marked "X14" but it might have other markings,
Any of these can cause HC and other Gemini issues.?? Get back on the Gemini version you have and if you are handy with a multimeter i can tell you where to probe to measure.?? If you have a bad "X14" you can jumper it with tweezers...if that gets the system working, you need to replace this fuse.? Get back we can advise on this
