A friend of mine offered up his family's old IBM PCJR (complete with second floppy, monitor, BASIC cartridge and Keyboard) for free on Facebook and I told him I'd take it.
So far, it doesn't seem to work. I stripped it down to just the motherboard, power supply and monitor and here's what happens when powered on.
The monitor lights up the CRT slightly grey and a roughly 200HZ square wave audio tone comes out of the monitor and nothing more.
The computer is capable of driving a composite NTSC display so I tried that and got no video. The audio tone from the audio out was still there.
Unfortunately this one has no socketed chips.
So it doesn't matter if I connect everything to it, or just run bare motherboard with power, the results are the same.
I've checked the external power brick and get the required 18V AC. I have a second power brick and get about the same reading.
The DC power supply board seems to work fine as well. I get all the required voltages on all the outputs and there doesn't seem to be any problems with load, burning parts, bad caps or anything like that.
Some random pokes around hitting the opposite corners of the chips usually gets me 5V readings.
Here's a high res picture of the board I found online:
http://bunniestudios.com/blog/images/ntw_nov_2012.jpgThe only thing I see that looks remotely wrong on the board is on my board, this little light blue part has a slight green tint on the bottom lead and the top lead looks darker. The blue part itself doesn't seem damaged or burned (this is not the picture from my board).
Do you think that's a resistor or another diode.

One more thing. At one point I had left the board on for about 15 minutes continuously and suddenly every so often, the cassette relay on the board would click a few times randomly it seemed.
I'd really like to get this guy going again. If you didn't already know, the PC Jr itself wasn't a commercial success only lasting a little over a year before IBM discontinued it. It had no ISA slots so you could not upgrade it using standard parts. Tandy pretty much cloned the PC Jr when they created the Tandy 1000, but addressed the issue of no ISA slots and the proprietary peripheral connections on the back (all .1 inch header connectors).
Where would you proceed next? I have not found a service manual with schematics unfortunately. There is a "technical reference" manual here :
https://archive.org/details/IbmPcjrTechnicalReference (or here)
http://www.retroarchive.org/dos/docs/ibmpcjrtechref.pdf but it doesn't seem to address the kinds of issues I'm seeing or provide any board level troubleshooting. However it does have some block diagrams. Here is a general IBM PC repair manual
http://ibm-pc.org/manuals/ibm/5150/Pcsim1-9.pdf