I plugged it in, like a kid on christmas expecting something extraordinary, and again NOTHING. So I decided to whip in a Mac IIfx ROM SIMM, remove the jumper, and see what happens. Interestingly, it made a startup sound, followed immediately by a crash sound, no time in between. This verifies some of the hardware including the processor and sound circuits and tempts us because we see a sliver of life peeking out at us.
The ROM select jumper makes no difference, it behaves identically in any situation I could conjure, with and without that jumper in place.

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The ROM chips on the motherboard have Chip Enable pins which must be tied low in order for the chips to work. I'm pretty sure that's all that jumper does. It ties the Chip Enable pins to ground. If you explore the chip enable pins on the ROM chips with an ohmmeter you'll probably find that they're connected to the 5V supply by about 3 - 5 Kohms and also to one pin of that jumper either directly or through a very low value resistor. The other pin of the jumper is probably connected to ground.

So, without a jumper, the Chip Enable pins are tied weakly high. With the jumper the ground connection overwhelms the weak 5V connection.

I can't remember if the IIci uses a 28 pin or 32 pin ROM. If 28 pin, then pin 20 on the ROM is CE. If 32 pin, then pin 22 on the ROM is CE. Orient the chip with the notch at the top. Looking down from above, pin 1 is the upper left pin. Count to the bottom (pin 14 or 16), then start counting up from the bottom on the other side. The top right pin is either pin 28 or pin 32.

So, given the symptoms you're experiencing, I would guess that there's still a munged connection somewhere. It might not be in the scratch on the board. It could be that leaking capacitor juice ate through a via or solder connection which is stopping the on-board ROM from operating properly.