The resistors have nothing to do with the high speed setting, only the slower speeds. The resistors provide resistance in the circuit, dropping voltage to the blower motor to slow the motor speed down. On high, the blower receives full voltage through the blower relay. If you had High but no other speeds, then the resistor pack is usually the culprit.
If you have all other speeds but high, the most common problem is going to be the blower motor itself, relay, or the switch panel. You can check this by turning the fan speed to "high", unplug the blower motor, and check to see that you have roughly at least 12v at the plug. If you have 12v, that means the switch panel is activating the relay and the relay is working. Over time, heat kills the magnetic properties of the magnets inside an electrical motor. Without enough magnetic energy, you may not get enough opposing force to spin the rotor full speed when the windings energize, but still enough to spin at lower speeds.
Another thing you can check is the connector at the blower motor and the switch panel. Sometimes these will heat up, start to deform, and cause a bad connection. The bad connection may be able to handle the lower current draw on low speeds, but the higher resistance from the bad connection won't be able to handle the higher current while in the full speed position.