A remote diagnosis is difficult, but here are some things to try.
First of all, did you connect the cable from the portrait display (mentioned under your Need a video cable for Macintosh iici topic) to the built-in DB-15 video port of the Macintosh IIci, or is there a separate video card that was used for the monitor? Has this monitor been tested with another computer? Has the monitor ever displayed anything?
Do you have access to another monitor supported on the Macintosh IIci for a test?
If Nubus cards are installed, remove them before tests. Also, remove any RAM modules not required for the basic function of the computer.
Did you check the logic board battery voltage (3.6 V)? If necessary, replace the battery.
Any change if you disconnect the power to the internal hard disk drive or to the floppy drive? Have various DC voltages been measured with a multimeter (under different operating conditions)? Unusual sounds from the power supply?