Are your ESCs set up so that center is off, one way is reverse and the other way is forward? You need this. This sounds like one of your several problems.
What FC are you using?
What "flight" mode switch position are you using?
Did you Upgrade and Erase so that your FC firmware version matches the GCS version? That is required.
With battery plugged in and USB connected to GCS, you should be able to go to GCS Input page and see the RC inputs change when you move the transmitter sticks. There can be a 1 second delay and that is normal.
You can also go to the output page and see what signals are being sent to the ESCs. You can also test the ESCs (Test Outputs on this page) to make sure they make the motors run like you expect, but be careful because the motors will run.
With USB plugged into FC, do File->ExportUav... and attach that file to a reply here. That is your settings for us to look at.