That's roughly 12-16 hours work assuming 5-10 minutes per machine. Worst case, first pass. And you can improve on it pretty easy. If it were me, I would do a first pass check: "who has a heart beat?" Just blast through them and eliminate the obvious duds.
Round up a couple, maybe few light, cheap monitors, some longer cables, and lug the whole mess into a room with some floor space.
Get a friend or two, setup some power strips, line 'em up, and plug them in. Do batches. Maybe 5 to 10 a pop.
Will they do anything useful on power up, even if that's to display some kind of status screen?
Best case is you plug monitor in and see that. Worst case, is you plug monitor and keyboard in and have to smack a key or something to see if they've got a heart beat.
This kind of first pass sort can potentially save you a lot of time. Put your focus into the functional ones and a better setup.
You can get this done in a day. Even if it's just you, maybe they only need a few minutes each, and you can overlap some of that by working in groups of several machines.
Get pizza, coffee, whatever and just bust it out. That isn't the whole task, but will give you the lay of the land.
While doing that work, formulate how to setup a more functional test bed. Offload that onto someone, or chip away at it for a couple hours each day. Or, bust that out too.
Have you got a deadline, or is this just a PITA?
If deadline, do the math and get help from somewhere, maybe from whoever stuck you with a pile of thin clients! And if it's you, well?
Just do it. Quick, dirty. Get it over with.
