If there is no "off the shelf" .... then this problem really calls for ingenuity and detailed knowlege.
Even if the pin-out details of a new ATX PSU and its supply volts and amps are known, you need similar data for the sockets on the motherboard.
Then there is a possibility by re-using the old power connectors with each conductor soldered and insulated. More a job for a frenzied geek or everloving engineer.
If you really cannot get a suitable matching PSU, (higher wattage is no problem) and cannot cannibalise one from a dud outfit, then you could consider a new motherboard using your P4 and more or less everything else? (There again will a new mobo fit your case?)