A common cause of this is poor power cable. You say you have a good PSU but what is the cable like? Telltale sign is a thin cable. If you have a multimeter you could measure the voltage on the RPi header (negative to pin 6, 9, 14, 20, 25, 30, 34 or 39), positive to pin 2 or 4). The measured voltage should be close to 5V. If it is less than 4.9 you may suffer. Try to measure this with all peripherals connected.
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