System must be full and purged of air before you can tell anything. You'll need to fill it with the bleeder screw above the water pump, and the one in the thermostat housing open, fill into the radiator, until no more air comes through the bleeders. Close everything up, and let it run for about 10 mins.
Let it cool off for about 15 mins, then open everything up and repeat. Once you have it full and bled, close it up, and start it. Take a drive and see if the problem still exists. If you run hot while moving, the fans are probably not the problem. The fans should run with the A/C on, provided it works. if the A/C comes on and the compressor is engaged, but no fan operation, there is definately a problem in the fan circuit.
The fans will fail to come on for a few reasons, but the most likely are sensing problems, due to air near the sensor, thermostat not opening so it doesn't sense the overheat, etc. I've seen them come in hot enough to cook breakfast on, and fans not running. After replacing the 'stat, the fans operated normally. Other problems with fans can be dead relays, sensors, and fan motors, but these won't affect both simultaneously in general, as they have seperate circuits.
In normal operation, coming to temp from cold, the thermostat will open long before the primary fan comes on. With the motor cold, start, and monitor the temp of the upper hose as it warms up. It should remain cool to the touch for several minutes, then begin to warm starting near the motor, and then have a sudden rush of temp as the 'stat opens and admits full flow to the rad.
The radiator will begin to warm at this point. Normally I'd have you run it with the cap off, so you could observe the flow, but I don't think you can see much into there because of the design of the neck on yours, you'll have to see. Check the temp at the lower hose going back to the water pump...if you can feel it warming at this point, you can assume at least adequate flow through the radiator. Most radiator flow problems will cause a car to heat when run at high speed, or prolonged idling. And they usually don't happen suddenly.
Once the 'stat is open, the temp should stablize, perhaps climbing slightly the longer it idles, but not more than 2/3 to 3/4 of the guage sweep or so. At some point (around 2/3 on most I've watched) the fan(s) will kick on, bringing the guage down somewhat, then turn off. Then the cycle repeats.
If you never get circulation (hoses and rad stay cool, engine gets hot, guage above 2/3 going to hot) replace the thermostat. If the stat opens, and flow seems sufficient (good temp in the upper and lower hoses, radiator fully heated) but it continues to heat up, the fans are suspect. But again, even with non-operational fans, it should run cool when moving, and begin to overheat when stationary.
My guess from the sudden nature of your problem, either the 'stat went bad, or the motor has been leaking slightly for some time, and finally developed enough air behind the thermostat to affect fan/'stat operation.
Recap. Fill and bleed. Test drive. Let cool. Check 'stat operation. Check fan operation.
There's a few other possibilities, but these are the common causes, and the quickest to diagnose.