What are you using for power supplies (power cords)?
The Raspberry Pi3 computers require significantly more power than previous models, so the days of using just any old 5V charger and cord are gone. You need a good power supply or charger and high current USB cable rated for 2A or more (recommended is 5V @ 2.5A).
Another problem with using USB chargers that require a separate USB cable is that many micro USB cables aren't rated for much more than 500mA, which is not enough for a Pi3 computer. So you not only need a good charger or PSU, you also need a good, low resistance micro USB cable to deliver the power.
The Raspberry Pi Foundation has their own branded power supply that output 5.1 volts at up to 2.5 amps that has a built-in power cord with 20 AWG wires (much fatter than most micro-USB cables).
Also, as a library, do you loan the Pi computers and power supplies out? If so, then it's possible someone has swapped your working units for their old broken one.
My mind is like a browser. 27 tabs are open, 9 aren't responding,
lots of pop-ups...and where is that annoying music coming from?