Well it's been 24 years since I fixed Toaster Flyer systems for a living.. but does the Amiga boot up correctly by itself, will it run regular Amiga apps and games? If yes, then what happens when you plug in the Toaster/Flyer, do you get a TNR, Toaster Not Responding error? Is there any output from the Toaster's preview screen?
Quite a lot of the time, when we'd see systems come in for this, a thorough cleaning of the card edges and cleaning/blowing out with canned air of the mobo connectors would fix it. You might also try gently unplugging and re-plugging each one of the individual boards on the Toaster itself.
Because Newtek was always a little odd about servicing a Toaster, we would collect the various boards of several Toasters until we had pretty much a unit made up completely of defective boards and then send that in. Then we had a working Toaster full of known good spares. We did this because it was difficult to cajole Newtek into sending us individual module boards.
I do not know if Newtek could or would still repair a Video Toaster or Flyer, as to them VT now pretty much stands for 'Vietnamese Television.' (I read up on them a couple years ago, they're really huge in that market with both hard and software).