Hi RDGC_member
Please note for Deep power-down mode, All clocks, the core, and all peripherals are powered down. Only the WAKEUP pins are powered. All functional pins are tri-stated in deep power-down mode except for the WAKEUP pin.
Please use WAKEUP pin wake up LPC804 from deep power down mode.
There is power_mode_switch_lpc demo code under MCUXpresso SDK folder, I suggest you referring it for the low power usage.
Thanks
Jun Zhang