if you get busy, hang up and retry. It will never go from busy to ring - it's a phone company thing. They check the status of the line, only supply ring, busy or not in service recording - it will never switch from busy to ring for that call.
If you continue to get busy after the 10th time, you were not quick enough to be one of the first ... x callers.
If you have multiple phone numbers you can call from, as they start to play the song or announce the contest, start calling, one line after the other, each time after you get busy, hang up and restart that line.
If your phone waits for dial-tone or is on speaker, it often dials more slowly than if it isn't on speaker.
If it starts to ring, hold onto that line, and listen, but continue to dial on other lines. You may be one of the first few callers, each gets answered, with which number you are. You might get lucky to get 2 lines into the answer sequence.