Let's deal with the easy bit first.
To open the 9810, open the flap on top over the printer paper hole. Then undo the 4 screws you see there. The top cover can then be pulled up by the flap and will come off.
You can now see (from the left) : The memory box, which is held down by 4 screws. If you need to work on that, take out the screws, then eject its backplane from the main backplane (read and purple ejector handles). Take off the side plate from the memory box (4 more screws).
Next, in the main machine, are the 4 processor PCBs.
Then the printer, next to that is the card reader interface.
Then, on the right, are the PSU boards. To get to those, take off the cover (7 screws IIRC). There are no particularly nasty voltages in there -- the mains is fed to a transformer at the back, and only relatively low voltage AC (30-0-30V I think) is fed to the PSU boards.
The keyboard comes off by the 4 screws on the bottom of the machine. It's connected by an edge connector under the printer and a 5 pin connector carrying the mains switch wires. You need to remove it to get to the printer, card reader, card reader controller and display PCBs.
OK, now how to debug it. It's not a trivial machine to work on (I speak from experience here), it's bit-serial, so everything should be changing all the time. To be honest, unless you have a 'scope and/or a logic analyser, you've got a lot of work.
To get something on the display, the CPU, ROM, RAM, memory controller, and display boards all need to be working. That's most of the machine!
I would start by checking the PSU -- all 6 outputs. 5 of them are on testpoints accessible through holes in the PSU cover. The 5V rail is marked on the display PCB (or just find a handy TTL chip on one of the boards :-)).
If they're all OK, I'd remove the printer, card reader controller, I/O backplane, any memory expansion board (red/blue handles, very top slot of the memory box), I/O backplane (at the back, behind the printer, it just pulls out) and disconnect the keyboard signal edge connector. The machine will run without those, the aim is to get a display.
If that doesn't help (and alas it rarely does), I will talk you through sorting out what the processor is doing. We had a little thread about this a few weeks back here that might be worth reading.
Finally, HPCC has reverse-engineered schematics for this machine, should you need them.