This is usually a symptom of a blown chip fuse. I have encountered and repaired this issue in multiple ESX's which had the same symptoms as you described ( LCD and tube backlights light up, but nothing else on the unit works). Earlier SN electribes were produced with lower capacity chip fuses than they eventually determined were necessary, and are known to blow said fuses during normal operation, so this is a common issue with these models. You can test to see if the fuse is blown by checking connectivity with a multimeter. Repair of a blown chip fuse requires replacement of the bad part with one of the same size (1206) and correct, updated value (1.5A). I have replaced this with littlefuse 046601.5NR fuses obtained from mouser with reliable results.