Hi 69er
Here's some ideas gained from recent overhaul of my Beomaster 5500 and a similar issue on a Beomaster 5000
No display / no or random microprocessor activity was caused by a failed capacitor responsible for STARTUP RESET. On the Beomaster 5500 and 6500, this is a 33uf capacitor designated C10 on microprocessor PCB 4 (4C10)
On both of the machines I worked on, significant degradation of 5V standby components had occurred, especially the capacitors. I also found an exploded capacitor near the microprocessor on the BM 5000, along with a cooked PCB near the standby bridge rectifier on PCB 2. The large 4700uf capacitor (2C15) is likely to have survived OK, but the small 10uf capacitors (2C14, etc) near the voltage regulators are more likely to have weakened.
Also, any Radial type black capacitors marked "ROE" (for Roederstein) are likely to be failing and should be replaced.
You may have noticed the giant coin cell battery near the microprocessor. This will probably still be putting out 3.2v and merely holds presets in the static RAM. I would leave it alone if reads at or over 3v.
What type or brand of capacitors to use? There is much debate and disagreement on this topic, with many insisting upon using only 105C caps or Film caps where possible, but I have noticed that Bang & Olufsen tended to use "Low Leakage" caps in many places, so my go-to caps are usually Nichicon UKL for low-leakage types, (orange Elna or Rubycon, many ROE caps) or Nichicon UVR for other 85C rated caps. A 105C (221F!) capacitor should only be replaced with a new 105C, of course.
It is OK to replace the Axial lead caps near the microprocessor with easy to find Radial lead ones so long as the ratings are the same and you avoid shorting the leads.
One checks the 5V standby voltage at connector 2P14, pin 2 (edit: pin 5) (on PCB2) to ground. it should read about 5.1v. Pin 1 is nearest the back of the unit.
When you get the microprocessor active, it is important to check the idle current on both channels. It should read 11mv across the emitter resistors at 0 volume with no speakers connected, but this is getting ahead of fixing the immediate problem....
Good luck!