The second time I turned it on the switch tripped.
I'm not sure what that means - are you referring to the fuse on the analog board?
I'm assuming you've decided against replacing the whole analog board with one scavenged from a Plus. In that case, a copy of "Macintosh Repair and Upgrade Secrets" would probably be helpful, as Blinkenlightz suggested earlier. I know you're working off the Dead Mac Scrolls, which I haven't seen, so I can't really compare the two. Macintosh Repair and Upgrade Secrets has a full chapter (15 pages) on diagnosing dead sets - ones that do absolutely nothing when powered on, including schematics of the relevant circuitry that you can use for troubleshooting. It also has a table of every part on the analog board, with a list of possible replacement parts. I was able to find a used copy of the book for $4.
Do you have any evidence of burning or blackening in the video section, in the upper half of the analog board? This is his first diagnostic test.
Assuming the video section looks good, Pina's first suggestion is to check Q11 (which is labeled Q10 on the international board). This involves desoldering it from the board in order to test it. According to the book, if you measure the resistance between pins, a good part will be infinity between emitter and collector (in either direction), about 650 ohms between base and emitter in one direction and infinity in the other direction, and about 650 ohms between base and collector in one direction and infinity in the other direction. A bad part will measure about 150 ohms between the base and emitter in both directions.
His second suggestion is to check R52 (R55 on international board). On the international board, this is a 20 kOhm 1/2 watt resistor, 5% tolerance. Also check R46 (1W 22 ohm, in-circuit reading should be between 18-20 ohm), R47, R49, and R50 (all 1/4W 1.5 ohm, in-circuit reading should be about 1 ohm), and R51 (1/4W 15 ohm, in-circuit reading about 12 ohm).
Pina also suggests checking Q8 (test the same way as Q10) and CR21, as well as the power switch itself, and the power cord.
Photos
You may also be dealing with damaged traces on the circuit board. If you see any that look damaged, try testing the continuity between the two ends of the trace to make sure it reads 0 ohms. If not, you can try repairing it with a wire.
It might also help to post some high-res photos of your analog board here, to see if anyone else can make suggestions based on visual inspection.
Keep in mind I've never done this myself, and I'm just parroting what's in Macintosh Repair and Upgrade Secrets.
