Some idle thoughts:
1. You have tried fiddling with the brightness button, etc.?
2. You could confirm that the vram and graphics circuitry on the logic board are working by attaching an external display (assuming you have the requisite adapter).
3. The usual advice in cases of LCD malfunction is to disconnect and reconnect all ribbons, so as to make fresh connections. However, there are new suggestions cropping up here and there these days that many of the problems in vintage LCDs relate to failed electrolytic capacitors. I cannot off the top of my head recall how many capacitors appear when the 540c LCD is taken apart (I have done it now a couple of times), but I do recall that there is a lot more in there than just the screen itself.
The simplest thing would, of course, be to source a replacement LCD — or to take the parts move in the other direction by parting this unit out, selling the 36MB chip and the SCSI drive and buying a whole new 540c with the probable proceeeds. I'd try 1-3 myself, as I tend to think that parting out collectable machines that can easily be fixed is a mistake.