Which port have you plugged the display into. There is a HDMI0 and HDMI1. The left-hand connector (when facing the back connector panel) is HDMI0 which you want to use.
When did you purchase the Pi400 from Adafruit?
Is there anything else attached the Pi400?
Can you try powering another device with the USB-C power supply to confirm it is working?
What are the LED colors and patterns?
When booting from an SD card, the Raspberry Pi's green ACT light should have an irregular blink. However, it can blink in a more regulated manner to indicate a problem:
3 flashes: start.elf not found
4 flashes: start.elf cannot launch, so it's probably corrupted. Alternatively, the card is not correctly inserted, or card slot is not working.
7 flashes: kernel.img not found
8 flashes: SDRAM not recognized. In this case, your SDRAM is probably damaged, or the bootcode.bin or start.elf is unreadable.