I HAVE A hp a712n, I turn it off the previous day and when i turn it on the foolowing day did not even beep, funs and lights are on
Try unplugging the system from the wall for a few minutes. If that does not solve the issue, try removing the battery and resetting the CMOS jumper to default system BIOS. Instructions for CMOS reset should be outlined in the system manual.
Uhmm sounds like a PSU problem. Try with another PSU.