My two bob's worth:
1. Establish exactly which model is which by looking at their serial numbers (inside the optical drive flap). Check them against Apple's database.
2. Try to establish what's wrong with the parts (other than monitor) of each eMac that don't/won't work. That may not be a simple matter, and your description is fairly general at this stage.
•Have you for example checked the state of the capacitors that can be seen through the RAM/battery hatch?
a sample eMac logic board pic is attached to show you the location of the capacitors.
•Have you tried booting from an eMac install disk, and running Disk Utilities to analyze the hardware?
•Have you checked the state of the PRAM batteries? Some Macs will not boot fully if the battery is dead.
I agree with others that your best option from the situation you've described is to use the eMac with a working monitor as your 'host' or recipient computer, and then put any necessary working parts from the other two eMacs into it.
[I will send you links to full technical eMac manuals if you PM me.]
Lastly, consider using an external monitor with any one of the eMacs that will boot and stay running.
This is what I intend doing, just as soon as the requisite mini-vga>vga adaptor arrives. My eMac monitor has discolored blotches at each edge of the screen, everything else is fine.