Here are the specs.. To be honest, I think you are going to have a poor playing experience for minecraft.
Seeing as you are on a P4, there really is no upgrade path I can recommend for you. You'll need a new motherboard to support relatively current generation CPU, which means you'll need new RAM, and probably a PSU and you'll want some discrete gpu. I would start from scratch and buy\build a new PC. Sorry
Minimum Requirements:
CPU : Intel P4 or its AMD Equivalent (AMD K7)
RAM : 2GB
GPU : Intel GMA 950 or AMD Equivalent with OpenGL 2.1 Support
HDD : At least 100MB for Game Core and Sound Files
Recommended Requirements:
CPU : Intel Pentium D or AMD Athlon 64 (K8) 2.6 GHz
RAM : 4GB
GPU : GeForce 6xxx or ATI Radeon 9xxx and up with OpenGL 2.1 Support (Excluding Integrated Chipsets)
HDD : 150MB