If we are discussing a Phantom 1, I might suggest first downloading the manuals from the DJI web site.
http://www.dji.com/product/phantom/download
The manual will detail the sequence for starting up the Phantom and the sequence of flashes required prior to flight. Waiting a minute may not be sufficient time for the Phantom to warm up and this would be indicated by the proper sequence of flashes.
Second, a compass calibration may not have a bearing on whether the motors turn on. You may need to perform an advanced calibration by connecting the Phantom to a computer as detailed in the manual. Your sticks may not be functioning optimally insuring the proper start up or Combination Stick Command as described in the manual.
Third, being able to fly flawlessly one time and not being able to start up another may mean a loose connection in the transmitter or the receiver within the Phantom. A situation you seriously should avoid, as it may occur when you are flying.
Start simple, place the Phantom on the ground, make sure the switches on the transmitter are in the correction positions, turn on the transmitter, plug in the battery on the Phantom and leave it alone until you have seen all of the flashes as indicated in the manual and finally start the motors. Fly up three feet and then land. Repeat this over and over until it flies without a failure. Fly no higher than three feet or so. Check all stick movements to make sure the Phantom responds properly. Do you lose the LEDs either on the Phantom or on the transmitter? Is your battery connection solid?
If it fails, connect Phantom to a computer and follow the instructions in the manual. Then repeat the testing. If it fails, then you may need to take the Phantom apart.
HOWEVER, if under warranty contact the vendor from whom you purchased the Phantom and seek repair or replacement before attempting any repairs. Explain what you have tried and how it has failed.
Remember too, some of this testing can be done without the props installed on the Phantom to reduce the risk of damaging yourself, the Phantom or losing the Phantom in a flyaway.