The monitor is a E173FPb - which transistors are we talking about ?

You mentioned 4 transistors that could be the issue of the screen staying black with the power monitor LED blinking Green but you did not state which ones to look for that maybe damaged. Are they the small C5707 ? These are the only one's I can find that are a set (2 sets of 2: Q739,740,759,760).

One set reads short ( .6ohms) between Base and Collector the other set does not. Emitter to Collector reading in only 17ohms vs the other set reads 35 ohms. Seems like an issue but without a schematic it is hard to tell.

Viper-Xp