Hello @Homunkulus,
The first thing I would do is double-check that all power connections in the system are attached securely (no loose connections between each module and its power cable, each power cable's connection to the power supply ribbons, the ribbon cables' connections to the power supply, and the external power connection to the power supply) and oriented the correct way at those connections (if the ribbons don't have shrouded headers, then make sure that the red stripe is on the same side as -12V).
The second thing I would check is the power specs of the specific power supply you have (mA available on each of the +12, -12, and +5V rails) and compare that to the total load that all of the modules you have connected to it in your case. The load of all of your modules together needs to be below what your power supply can provide with some extra headroom. The amounts I hear people mention most often for this excess headroom is 20 - 30% of your power supply's maximum output. For example, if your power supply can provide a maximum of 1000 mA on each of the three power rails (1000mA @ +12V/1000 mA @ -12V/1000mA @ +5V) then you should only connect modules that need 700 - 800 mA total on each of those rails. To my understanding, this is because many modules draw more mA when first powered on than what they need to function after being powered on (which is likely what the specs provided for most modules are). Also, if your power supply relies on using an external power brick, make sure it has the appropriate wattage/voltage/amperage specs for the power supply. If the power supply accepts a range of voltages, you can try a power brick with a lower voltage within that range to get a higher amperage output (but the wattage must remain the same) Amps x Volts = Watts. It can also be useful to know if the power supply you are using splits up its power output in any way. For example, if there are two headers for ribbon cables on your supply, it is possible that the power supply's total output is divided between those two headers, so you may need to redistribute which modules are connected to each of the ribbons for a more even distribution of power draw. All of these specs should be available in the manual for your power supply.
I hope some of that helps!
Chace