I tried to make nougat but just could not get to the hard ball stage.
It's not a question of "how long" as much as it's a question of "how hot." Sugar reaches the so-called hard ball stage somewhere between 250 and 265 degrees F. How long it will take your sugar to reach that temperature depends on a number of variables including the power of your cooking range and the type of vessel the sugar is being cooked in.
Use either a candy thermometer or the tried and true water testing method from which the stages get their names. When dropped into cold water, the sugar will literally form a hard ball when rolled between your fingers.
You either did not apply enough heat or you applied too much heat. The most reliable way to troubleshoot this problem is with a thermometer.
There's some great information in this article titled How to Test Stages of Sugar on RecipeTips.com
Pictured below is the example image from that article of what hard ball sugar should look like when dropped into cold water: