I doubt it since the 24 pin version has 4 extra wires comming from the power supply. When you go from 24-20 the extra wires aren't used.
Also, I would advise against using a power supply from such an older system, it may not have enough power to run the P4 and it could even cause problems. It's always good to get a good PSU when making such a switch.
Yes, there are converters that take a 4 pin in line molex and convert it to a 4 pin square that. They were used whent eh 4 pin squate first came out. That gets the extra 4 power and ground wires to the conenctor. Many new MB's have the 24 pin and a seperate 4 pin square connector to allow for adapter.
The thing to watch out for is that the power supply provides enough +12V power. If you are doing top end 64 bit cpu and high end graphics an old PSU will not support it. That needs an ATX 2.0x power supply with minimum of 2 +12V rails rated 17A each. The higher end video you go or if you go SLI then requirements are even higher.
Post what you plan and we can make recommendations.
my current P4 3G is using a new power supply, it is 400W 2theMax model.
but it seen (may be) unstable because one harddisk always 'disappear' while turn on the PC. I am wondering the new PSU and so I want using my old P III PSU (300W)to temporary replace for testing, and then make decision on buying a new PSU (24 pin for P4 3G CPU).
because the 20-24 cable is cheaper. a new PSU cost me a lost..also i think to buy a 500W model.
Just remeber, as it has been said MANY times in multiple threads, when purchasing a PSU it's not only the wattage you need to look at, you also need to make sure the amperage ratings on the different rails are high enough (high the better).
Like LeeJend said, if you have a high end system you will most likely need soemthing with 17A or higher otherwise you make have issues.
The issue you described my be a sympton of an overworked PSU and using something thats rated for a P3 won't help with troubleshooting as it's ratings may be lower then your current one.
Probably not. It depends on what processor and video card you have. The PSU you have is intended for older processors and video cards that used much 3.3V and 5V. The new P4, AMD 64 and dual core processors need mostly +12V. The new video cards use much +12V also.