This HP-55 was baffling me for a while. Initially, the unit was completely dead, but I found the cause easily: a the legs of a transistor in the DC-DC converter were crushed. I replaced it with a 2N2222A and the unit fired up, sort of. When I turned the unit on, only a few segments lit up faintly; however, they flickered in response to keystrokes, and I was even able to write a simple program blindly and watch the flicker as the program executed. Because of this, I suspected the display driver chips and I actually replaced them both with great difficulty. To no avail; the machine still wasn't working. Eventually, I began to methodically check all discrete components on the main circuit board and I happened upon a diode that was open. When I replaced the diode, the calculator fired up and it's been working flawlessly ever since.
Dead HP-55