Alright... I'm now in the possession of the PCjr!
The machine powers up, beeps twice and then displays nothing through the composite video jack. The computer's purchase came well documented, and oddly enough, it has apparently had this trouble before. There is a repair ticket (from ComputerLand!) and the problem statement says, "fan comes on but nothing on screen" and the resolution was to replace the motherboard, under warranty (retail price $450).
It also has invoices for when the computer was purchased and what was included. The parallel port attachment they paid $88.11 for, the Enhanced model PCjr was $999 (January '85), and came with PC DOS 2.1 and Cartridge BASIC.
I haven't tried using the PCjr color monitor with it, just my TV through the composite video jack to troubleshoot.