Hi,
Can you post a little more info regarding Chassis (what wiring loop it has), CPU, PSU, Memory brand and rating, Graphics Card, HDD's etc., as it could help pin-point a problem.
Just because some of the LED's come on doesn't mean that your PSU is OK. I've had brand new PSU's that have been dodgy.
You can build outside of the Chassis to make things easier and it will work but be very careful if you do this.