Take everything out except the roms, cpu, and led pia, then use a logic probe to check if all the inputs to the pia are functioning.
Could also be a bad clock for the cpu

LED is on U11. Check everything on the left side. I would expect everything except the bottom 3 to have activity. (and maybe 37+38)

Alright, back to the CPU checking activity. You should see movement on 3 and 37 from the clock (coming in from U15), or else the CPU won't run. If it's running you should see activity on the Address and Data lines

Do you have any other working MPUs you could compare with? The clock signals are fragile enough that sometimes just reading them with a logic probe will mess them up, but usually it's fine. If the clock circuit isn't sending the proper signals into pins 3+37 of U9 then the CPU will never start. Probably U15 or U16 is bad, but they're both hard to come by

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U15-8 should be the inverse of 9 and 10, so I think it's definitely part of your problem, unless something has shorted pin 8. Can also try reading pin 8 with the CPU removed to see if that changes anything.

OK cool. Now go back to checking the pia inputs

So, CPU is now running and sending commands to the other chips, but the PIA isn't getting the specific command it needs to turn off the LED... Is this with just the ROMs, U11, and U9, or do you still have other chips installed? If not, I'd suspect the rom jumpering first of all (what rom types are you using?), otherwise something must be messing with the address/data lines..

It looks like E13-15 aren't jumpered to begin with in your original picture? What's that one wire on the back?

I guess you should check the pins on the other chips then. Roms should have activity on 1-11, 13-19, 22,22. Low on 12, high on 24.

CPU should on all the A and D lines, as well as 34 and 5

Oops. Should be 22, 23.

With your specific jumpering (E12 - GND) that's correct.

what do you mean by "high and low on"?

This seems weird. This pin on U9 should be connected directly to the D1 line on the roms (pin 10) and PIA (pin 32), both of which you said had activity. Do you have good continuity between all of them? Maybe a bad socket or trace somewhere...

It should be pulsing at all 4 places. If it's not you might have a short somewhere or something. I even have one board with a problem like this where somewhere along the pcb the trace is actually cracked, so if you flex it it'll read different :/

Not from U15. All the Data line should be pulsing pretty much constantly. Different chips drive it at different times.

Anything on the data line could cause it. Ram, rom, pia, etc. Or stray solder.

You could try taking out all the chips, and measuring resistance from each Data like to ground, see if this one has a different reading. If so, you'd know it's not one of the socketed chips.