Just as a last check, open your case and watch that fan closely right when you first boot up. Normally any fan connected to a mobo fan headed will start up at full speed as soon as you boot, but will slow down in a few seconds and MAYBE stall. If you fan does NOTHING - not even a little "twitch" at boot time, it is probably dead.
However, IF that fan is NOT connected to a mobo header - some in an AIO system are plugged into a different place - this may not be a good check test. IF it's plugged in differently, tell us the detail. There is another test you can do on the fan using an auto battery as a 12 VDC power soucre, and connecting that to the correct pins of the fan. To do that you would have to remove the fan first to get it to the battery. If you want details, post back here.