my p4 3ghz fan on top of the round metal heatsink has 2 plastic propellers missing (broke off) but there are still a good few bits left. is it safe to run it like this?
not really, have you applied a paper thin layer of thermal paste between the CPU & HS/F ? BTW: what is actually broken (HS/F)
well, it's hard to say w/o us knowing how the case is vented, the workload of the CPU, the heat dispersion of other components (RAM, VGA, South/North bridge)... the best would probably be to check out the temps with this program. but my wild guess is - no - those P4's tend to heat up even with a intact cooling system (mine idles @ 36C* with a okay vented case...).
From my experience, P4 are hot (but not as hot as AMD k7's). No, it's not safe with the broken fan, because it will be 3x less effective and seriously damage your CPU even at maximum RPM (which i am assuming is 3000). You need to buy a new fan or fan+heatsinker. Ventilation around your case is no use if there is hardly any hot air comming from the CPU fan in the first place. Also, P4 demands that you have a case with ventilation gaps directly above the processor (drill holes or a funnel), and a fan at the back to let air out.