Got a HP8563E (26.5GHz). That doesn't start up. Does this:
This is a variant of SMPS "Tick-tick" failure. One or more rails has a short, and it is exhibiting a startup/voltage test/shutdown failure repeating cycle as a result.
Since LEDS indicate all rails are coming up for a fraction, my guess is there's a fault in one of the rails on the load side; something that only shorts once an active component is energized. Usually if the fault is in the PSU, one of those LEDs will stay dark, indicating the faulty rail.
First order of troubleshooting will be to disconnect PSU from all the main rails & see if it comes up all the way. Alternate potential fault is one or more weak filtering caps that cannot handle startup surge current. This is not as common.
Also, look for warm caps after it's been ticking a while.
mnem
*Quick & dirty*