Ensure there is power at the wall outlet where the machine is plugged in.
If there is a power switch on the power supply (at the rear) switch it OFF and ON two or three times.
Have you tried another power cord? (Wall outlet to P.S.)
Have you checked to ensure major components (CPU and fan, memory) have not become dislodged/loosened during the card install?
Have you verified all connections from the power supply to the motherboard? (All connectors fully seated)
You can check the power supply itself by removing the main connector from the motherboard and shorting pins 14(Green wire) to 13 or 15(Black wire) (or any other GROUND pin) in the main connector. See picture. If the P.S. fan starts, unplug it right away as it shouldn't run without a load on it.
If the P.S. starts with the above method, then check your connections from the front panel (ON/OFF switch, etc) to the motherboard header connector. See picture.
What is the make and model number of the motherboard?
What is the make and model number of the AGP video card?