I thought along the same lines IIO. Yet, if you cut the power end off of the Cinema Display you’ll find that there’s only two wires within that oval-shaped, proprietary Apple connector that plugs into that Apple “power-brick”. AND, given that you wouldn’t even be considering this alternative if your monitor was functioning properly with the Apple-made power supply… well, there’s no need for an Apple connector if you’re wiring those two wires (plus and minus voltages) directly to the new DC voltage PSU for the monitor, after you’ve cut that end off and exposed those two wires.. (Think the voltage requirement to the monitor out of the PSU is 24.5 VDC / 65-90-150 Watts... up to the later Cinema HD models.)
Now, the A1103 G4 Mini’s are a bit different, as they need 18.5 Volts and pull 4.5 Amps. The second alternative PSU pictured, does have an onboard “potentiometer” where you can adjust the voltage output to suit your needs, which might allow you to “dial-it-back” to 18.5 Volts output for the Mini. AND, if you’ve already cut the end off of a Cinema Display power cord… you could possibly wire that to another alternate source to provide power to the Mini. This of course depends upon whether or not Apple’s (10 connector-pins-inside) oval-shaped plug only carries the voltage of two wires delivering a 18.5 Volts.
I don’t know if the smaller, less-expensive power supply pictured has an adjustable voltage ouput option. But, I may purchase one of those first… even some of the Apple laptop “brick” PSUs can supposedly be used for the Cinema Display monitors.
As for the Mini… I’d even consider “wiring around” the normal oval-shaped power plug input, inside of the Mini… if it does not prove to be more than a single, two-wire-in/out power delivery system. Again, any cut-off oval connector(s) from Cinema Displays could possibly be used.
Originally, looking at that oval plug from the diplays with those ten, tiny pin-contacts inside, certainly led me to believe that there was indeed more “going-on” that just two wires coming in. Guess someone had to simply cut one off, first?