From searching around on Google, I can tell that this is a common problem for the Presario F500.
However, my symptoms are different. Others say that the LEDs come on, the fan whirs a little, but the laptop eventually shuts down. For me, it won't turn on at all - no LEDs, no beeps, no fan, nothing. The charging port light does come on, though. I've tried turning it on with just the charger, just the battery, and both.
It was working fine up until a little while ago, when I came home to find it wouldn't turn on. I don't rely on this laptop for anything major and won't be devastated if it's not worth repairing, but I would like to know if there's anything I could try.