Well, about all I can offer to this is maybe to help 1hookedspacecadet with Analog to digital and PS/2 controls.
Easy explanation - A PC joystick (Saitek, etc.) is analog - it uses potentiometers to sense movement. An Arcade joystick (Happs), is digital.
Generally analog joysticks are okay for digital games, but digital joysticks suck for analog games.
Example - play Tiger-Heli, Pac-Man, or 1942 on a PC Joystick. It works okay, even though the game is meant for a digital controller.
Play Star Wars or Sinistar or or Paperboy, or as Peale said Pole Position with a Happs stick on your arcade cab. It doesn't work well, because the stick is either up or centered, not 2/3 of the way up.
The PS/2 controller has 4 shoulder buttons, a D-pad, two joysticks, and 4 game buttons, and a start and select button. On the PS/2, the D-pad is digital, the two joysticks are normally analog (but I think can be switched to digital by a button) and the action and shoulder buttons are digital (I think).
Most games primarily use the left analog stick and the lower diamond button (the one with an X on it), but most also use the other buttons, right stick, shoulder buttons, etc. for more advanced controls.
I am not sure if you would need to swap/adjust the range of the pots or not, but it should be very possible to hook two PC joysticks into the pots for the PS/2 controller sticks. This gives you the two analog joysticks. (I'm not sure if you could also make them work digitally, but that shouldn't be a major concern.). The buttons are just a matter of soldering leads from the PS/2 controller button contacts to arcade buttons.
Setting all of this up on a panel so that Sean can operate two joysticks and eight buttons simultaneously with the heels of his palms will take a lot of work, but I'm sure the members of this board are up to the challenge.
At this point, it would be helpful to know what types of games Sean wants to play and what controls he would be comfortable with.
Not to completely change the course of the discussion, but someone mentioned MAME - This might be a better option - All it would take is something like the joystick that Stevejt (sp?) mentioned and some arcade buttons, and a $40 computer with TV out.
The reason I am suggesting this is two-fold - most MAME games are digital joysticks - ON-OFF means fine motor control is less necessary. Many MAME games require much less controls and coordination -
Pac-Man, Q-bert - Joystick
TimePilot, Galaga, Galaxian, Gyruss - Joystick and one button
Robotron - Dual joysticks, no buttons.
You won't find MAME games that need two analog sticks and 8-12 buttons, and that's a good thing in this case.
And (probably with some donated parts), a MAME system could be done for under $100. We'd need one of Paige's $30 computers, though. For that matter, Sean mentioned ViaVoice and is posting here, so assuming he is using his computer and not a central one at the nursing home, he probably could be running MAME, if we just built a controller.
I'm assuming also that Sean would enjoy classic arcade games, but who wouldn't (besides my wife . . .)