The wiring diagram looks correct for the 840.
I just downloaded your project files, it's looking really good for a first draft!
A few comments/suggestions, nothing critical:
1/ Is there a specific reason you chose an ATX20 header over a 24 pin one? PSUs with that kind of connector are getting old and I'm not sure whether you can fit a 24pin plug on a 20pin header or not. Maybe you can, I just don't know.
2/ The 22 pin header footprint on the Quadra side looks hand made? There is a built in Kicad footprint that looks quite similar to the one on the ATX side. I know from experience (QuadrATX 9x0 board #000) that it makes soldering those large connectors a breeze. Plus the larger the pad, the less likely it is to rip it off if you make a mistake.
3/ Speaking of footprints and default ones, the one you used for the Softpower transistor looks a lot better than the one I used originally, but the pads might still be a tad too close together? Especially 1 and 2. I would use TO-92L-Wide just to be extra sure.
4/ Do you really need that many VIAs for the ground plane? It's only power and you already have thermal reliefs on every GND pad...
5/ Do you need the trace that goes from J1-Pin7 to J2-Pin19?
6/ What are the J3-6 connectors for? Just curious...
7/ There are a couple 90° angles (5V trace on back copper). Shouldn't pose too much of a problem since again this is only power.
8/ The Q950 text should be removed (silkscreen)
9/ The silkscreen text for H1 and H4 is outside the board
10/ The resistor values for the LEDs aren't final right?
11/ Thermal reliefs could be a bit bigger
12/ J2 silkscreen inside a pad
13/ Are you planning on securing your board to the original metal casing? If so I wouldn't mix DC GND with AC earth and I'd replace the plated mounting holes with non plated ones.
14/ Just a personal preference but since the Quadra isn't using 3.3V, do you need an LED and traces for this rail? For the QuadrATX 9x0, I simply connected them to n.c.
15/ The -12V trace on the top (red) is all right, but it gets a bit too close to the 5V standby trace. The .2mm gap between them is still enough (17<30VDC) but why risk it?
16/ The GND copper zone failed in a few places. 3D Viewer is great to see that sort of thing!
That's all I can think of at the moment. Hope this helps!