Okay, based on your info, I'd say the problem is in the fan circuit and NOT a radiator, thermostat or head gasket issue, since the car cools off at higher speeds---this would not be possible if the latter items were defective.
Not sure what you mean by the fan "trying" to kick in. You could be hearing the relay clicking, which still might be bad even if it clicks...I'd go to the public library for a manual, or on eBay, and find your relay box and identify the fan relay...if there is another relay in that box with the exact same part number, you could switch them and see what happens. Either you or someone who knows how could "hot wire" the fan to the battery for a moment to test the fan motor. So you have temperature sensor or sensors, fan relay, and motor, and wiring---all of these are part of the system.
Also the fan, or a second fan, should kick in when you turn on the AC. You might try that while it's overheating, to see if the fan kicks in and if that brings the temp down. This way you'd know the fan was good and that your sensor, wiring or relay was the culprit.