Are there other baseboard units in the house? Do you know if this unit is wired for 120 or 240 volts? If it were 240 there would be a double breaker in panel. How long is the unit and is there a brand name on it?
It is possible for a baseboard heater element to outright burn out.
Sometimes it is not worth repairing but you could disconnect one of the two terminals of the element, turn off the power, and do a continuity check. The element when cold would measure somewhere around five ohms, although the most important distinction is that nearly infinite ohms means it is burned out.
You can also measure the continuity (or resistance) of the element to ground but you must disconnect both terminals. Less than a hundred thousand ohms means a fault significant enough to cause electrocution and the heater should remain disconnected until repaired. An element that works slightly has a high chance of having a fault to ground.
It is difficult to shop locally when the locality slaps you with a fine if you are a little slow getting back to your car.