Well it COULD have, but with thermal protection enabled on the mobo and on your CPU, it's unlikely. That's assuming your mobo thermal protection was enabled. Some people turn it off to test overclocks, and then forget to turn it back on. Not that I have ever done that... ahem.
Anyway, it should be pretty hard to burn up an Athlon 64 just by turning off the fan; they have their own circuit that should shut them down. That doesn't mean you CAN'T burn one up, just that through normal fan failure, it should be pretty hard.
Now, if the fan blew up somehow and your motherboard detects that the fan is not working or doesn't detect it properly; THAT could prevent you from booting up. Some mobos will require CPU fan detection before they will boot. I believe my DFI acts the same way if I forget to plug in the CPU fan, but I'm not 100% positive on that; it's been a long time since I mucked about with that.
Try slapping a new fan on there (and by that I mean plug a working fan into your CPU Fan header on the motherboard) pointing at your CPU and see if it will boot. If it does hit the BIOS and check your temps.