many times on such systems, the system fan isn't actually there...and can be ignored...though not really sure in your situation
You should be able to get into bios and tell it to ignore the error.
there may be something like "halt on all errors"
access hp bios by pressing f1 or f10 (mostly)...sometimes esc
in bios...load defaults by pressing f5 or manually locate settings yourself
NOW...I say the above, in that it COULD be ignored, but I'm not too sure on your system. Last place I worked at they had an old branded pc as the time clock, and it always had this error, I always had to hit a key to proceed. That machine seemed fine.
your system fan (whatever that actually is inside) may actually be dying. If you want, see which one it is and match it up...only about $5 I would say.
HP and Compaq Desktop PCs*-* Error: CPU Fan Failed*