When I power my Denon AVR-3311ci on, it only comes on for a second then shuts off completely. No blinking red light and nothing on the display. I can hear a relay on the power board clicking. Any ideas? This symptom isn't in the manual troubleshooting section.

Greetings
have you checked the speaker cables ?
please do
Usually the Denon system has a problem with power regulators
if u have any knowledge in electronics i can guide u to repair it
if not .. u have to send it to service.

check for fuses if blown
power regulators mostly are damaged
and or power output transistor damaged
Good luck From Audio-adviser.com

you most likely have a shortedchannel in the amp that would need to be repaired

These receivers have a history of having bad +/- 15v regulators. If one of these is out of tolerance, it will cause the problem you are having. If you are good with electronics, it's something that is fairly easy to check, otherwise you may want to take it in to have it looked at by a pro.

This is a protection mode. The receiver protection circuit detects an internal problem like missing power supply voltage or blown channel and shuts down the receiver. You need to bring the unit to a repair facility.

Take it to a hands-on tech. It's smoked.

SWITCH OFF THE UNIT..PUSH AND HOLD DOWN BOTH SPEAKER A AND SPEAKER B BUTTON WHILE HOLDING DOWN BUTTONS TURN ON MAIN POWER THE DISPLAY WILL FLASH WAIT FOR 3 FLASHES THEN RELEASE. THIS WILL RETURN EVERYTHING BACK TO RFACTORY DEFAULT

From my experience you need to replace the Hi power module

Hi...

1st thing to check is for GOOD speaker connections at both ends
and not mixing A and B speaker wiring.

A Denon is usually a good brand. Might be worth servicing if need be.

when i turn it on it stays on for 3-4 seconds then shuts down

I think Denon designed in a "bug" as mine just "went east" today