No the mobo is compatible with the Power Supply, and GPU.
You mean the Processor (CPU) fan?
I'm guessing I guess, because computer case fans aren't on the motherboard/mainboard/mobo.
You're getting power to the mobo, but the question is how much?
1) IF ALL of the LED lights were on at once, they would use less than 1 Watt of power.
2) EACH fan uses 2 to 3 Watts of power.
3) A typical Processor can use from 51 to 125 Watts of power.
Just depends on what Processor it is.http://22.214.171.124/app/en/mb/introduction.php?S_ID=363&tab=1
The mobo will support Intel Core2 Quad-Core processors. Depending on which one, you may be talking about Up To 105 Watts of power,http://en.wikipedia.org/wiki/List_of_Intel_Core_2_microprocessors#Quad-Core_Desktop_processors
This is why LED's can light, and fans may spin, but the Processor isn't getting enough power, so the computer will not turn on. (Processor isn't turning on)
1) Just because that Power Supply is new, doesn't mean it is good.
Sometimes you get a bad one. Test the three main voltages coming out, with a multimeter set to DC Voltage.
Need guidance post back in a Comment.
(An economical multimeter can be purchased, for as little as $8 to $12. I have seen cheaper. Available in a multitude of stores. An auto parts store is but one example )
2) You don't have the 4-pin ATX +12 Volt power cable plugged in.
Goes to the white square 4-socket hole connector, to the left top corner of the Processor socket.
(Motherboard installed in computer case)
3) REQUIRES -> TWO 6-pin PCI-Express power cables, for the Nvidia GTX560Ti graphics card.
The Antec HCG750 PSU has 4 of them, so no problem there, IF you have two of them plugged into the graphics card.
Both connectors of the 20 + 4-pin ATX main power cable's connector, need to be used. Biostar mobo requires a 24-pin ATX main power cable.http://www.newegg.com/Product/Product.aspx?Item=N82E16817371049
Post back in a Comment as to power cables plugged in, and DC Voltage test on PSU.