I will repeat - power supply.
First, have you tried pressing the SMU reset button? It's one of the reset buttons, near the LEDs that you mentioned. The SMU is the lower of the two. Press and release (with no power or any other cables attached), and that's all you can do. Put your iMac back together, and try the sleep again. If it simply shuts off, then get a replacement power supply.
If you only have a single button inside, then reassemble, and leave all cords disconnected. Reconnect the power cord, while you simultaneously press and hold the power button. Release the power button, and attach your keyboard and mouse, then power back up. Check your sleep again. If it just shuts down, without sleeping, then I still will say 'power supply'