Well it is possible that you didn’t plug in the 4pin ATX supply from the psu to the motherboard, and that caused some problems, but I assumed you knew which plugs from the old one went on and could go by that to connect the new one. The new connector is probably 8pin by the way, or 4 + 4, but will fit the 4pin socket on the motherboard.
There are some differences between modern psu’s and the old ones, but that is primarily amperage on the 12v lines. However, there is less wattage on the 3.3 and 5 volt lines on new power supplies compared to the old ones and very old systems rely more on those rails than new ones. Also, the -5v line has been dropped almost entirely since it is so rarely used on modern systems. If you have an old computer that needs it however, it might be a problem when putting in a new psu.
Check the figures on the 5 and 3.3v lines on the old psu and compare them to the new one.
Edit: By the way, your system is new enough it shouldn’t be affected by the -5v line absence, and I’d be a little surprised if the values on the 3.3 and 5v lines from the Enermax would be enough to cause problems on a P4 system either. So, I’m basically just shooting in the dark trying to figure out why it isn’t working on your computer.