It's hard to say exactly what the issue is, it might just be that your motherboard is dying and no longer detecting the fan speed properly, or maybe it's just that your fan is dying. Does the fan spin freely if you try to spin it yourself? Is the fan actually spinning when you turn on the PC and it displays the error?

Since your fan seems to be working it might be your motherboard, but you should be able to ignore these errors by entering into the BIOS and looking for the option "Halt on errors" and switching that to "None" or "Off". This will keep it from sitting at the BIOS screen waiting for you to press F1.