On an electric cooktop that uses surface element switches to control the elements, a failed surface element switch can prevent the surface element from heating. On electronically-controlled cooktops, a failed surface element relay on the electronic control board that controls surface elements can keep a surface element from heating.
No matter which type of control your cooktop uses, a broken surface element won't heat. If your cooktop uses coil surface elements, examine the element that isn't heating and replace the coil element if you see a cracked or broken coil. Radiant surface elements are harder to check for damage because they're under the glass cooktop. Unplug the cooktop and remove the burner box to access and check a radiant surface element that isn't heating. Replace the surface element if you see a break in the ribbon element.
A radiant surface element has a limiter switch that cycles the radiant element off to protect the ceramic glass cooktop from overheating. A failed limiter switch won't allow the radiant element to heat. Disconnect electric power to the cooktop and check for continuity through the limiter switch using a multimeter. You should measure near 0-ohms of resistance through the limiter switch indicating that the switch is allowing current to flow through the element. If you measure OL or "open load" indicating that the switch isn't allowing current to flow through the element, then the limiter switch has failed. The limiter switch is often included with a radiant element but not always. Replace the limiter switch if it's a separate part and it's preventing the radiant surface element from heating. If the limiter isn't available as a separate part, replace the radiant surface element.