After messing around more with the Agilent, it seems like there is an issue with the motherboard.
I powered everything off of a lot of lab bench power supplies. After powering, nothing appears on the screen. All four LEDs on the CPU board are lit. The 5V rail seems to be drawing 5.6 amps, while the 3.3V rail is only drawing 0.5 amps. The manual claims that this might be due to a bad bootrom, or due to an issue with the reference assembly.
Here's what the manual says:
If the screen remains blank (dark) and the green LEDs never blink, the
instrument was not able to boot from bootrom. The bootrom on the CPU
assembly could be bad, or the instrument clock signals could be
missing. The bootrom is not a replaceable part.
If the 30 MHz sample clock from the A8 Analog IF assembly to the A7
Digital IF assembly is not present, the display signal processor chip on
the digital IF assembly will not reset, causing the PCI bus to hang up
and the instrument will not boot.
To check the 30 MHz sample clock:
• Put the A7 Digital IF assembly on an extender board (E4406-60021).
• Check A7J4 for a 30 MHz signal using an oscilloscope, as shown in
Figure 6-1 on page 142.
• If the signal is not present, the cause could be the A8 Analog IF
assembly, or the A11 Reference assembly. Go to "A11 Reference
Assembly Description" on page 118 to check the reference assembly
Also, judging by the number of connections going to the processor board for VDL (3.3V) and VCC (5V), it appears that the 3.3V rail is relatively low current, since 3 or 4 times as many pins are used for VCC.