Well, to bad I didn't see this earlier, or I would have given you the standard advice. Always replace CPU, MB and memory as a unit. That is the sure path to success.

Your P4 is so outdated that it isn't funny. Hyperthreading in the P4 was so much of a joke that it was removed from Core 2. It's back in Core i7, but it's completely redone and actually works.

You can buy a CPU, MB and memory for under $100 and have something that is about four times as powerful as what you have now (well, you'll likely also need a new power supply). I prefer Intel, but AMD is certainly cheaper and that sways a lot of people.

But now to something that might actually help. I hope.

Is the speaker connected? That's an important piece, since it will beep on POST errors. If it's connected and you get nothing, it is likely a bad CPU. Most other faults will elicit beeps from the speaker. The pattern of beeps has a meaning that should be described in the motherboard documentation.