Reasons your motherboard might not power on in the new case:
1.. Defective power button on the front of the case.
2. You didn't install the motherboard properly in the case.
(short out the motherboard power pins with a touch of the screwdriver. if it works then you know there's no short from the case, motherboard not grounded)
3. In the new case, you didn't connect the wires properly from the case to the motherboard front panel header.