A brown-out indicates that the power supply (and regulator, and the circuit connecting all this to the load) isn't capable of supporting the load being placed on it.
Yea but that doesn't explain why the normal batteries have the same problem. I understand the use of the Main capacitor, to get rid of any voltage spikes or dips. But if the power supply doesn't have enough current to supply to everything as it is, then the capacitor won't have enough charge to do its job.
Yeah, if the power supply can't supply enough current, that's certainly needs to be fixed. I thought OP was using a huge old PC supply.
I imagine there's a lot of brownout protection cktry inside the computer box.