I'd begin by looking at the fuse box on the top of the battery. The middle of the three fuses is responsible for controlling the engagement of the fans. If something spikes the voltage in that circuit, it can take out the fuse — disabling your fans (and the A/C compressor by association, I'll get to that in a moment).
When the A/C is on, the first of the fans's two speeds are constantly running when the car slows down to a certain speed, or stops altogether. This is to keep the compressor cool (it generates buku-heat n' could burn itself out otherwise).
If that fuse blew, the car was designed to not operate the compressor if the fans were inoperable (for fear of compounding the issue w/ a broken compressor — also, your A/C being out is a good way of letting you know this may have happened). When your car is at risk of getting hot (which it will without properly working fans), so will you.
If it isn't the fuse, the next likely culprit is the fan control module below the battery. This controls all functions of the auxiliary fans. I'd bet a nickel or two that if you pop that fusebox cover on top of the battery, you'll find a toasted fuse though.
If you do, that doesn't necessarily mean that's the only thing that needs replacing (by the way — if the fuse burnt out spectacularly enough, the whole battery-top fuse panel may need replacing). The spike in electricity could damage the fan control module too — in fact, any electrical device connected to that circuit could be at risk of damage if voltage spiked.
When this happened to me, I ended up having to change the fuse box on the battery, the fan control module beneath it, and I even changed the fan thermal switch (located in the passenger bottom corner of the radiator). The fans themselves appear to be working properly, so I lucked out there.
After you replace what ever's necessary to get the fans to kick on again, keep an eye on the coolant temperature, and it may not be a bad idea to make sure too much voltage isn't being pulled by the electrics of the cooling system — just to make sure there wasn't something else that caused the original parts to burn out in the first place, and will toast the new ones too.
Good luck, cap'n.