This is not a good idea. Here's why.

1. Power.

A P3 didn't need a lot of Watts from the power supply. You'll want a new whopper power supply to stay out of trouble. Try 450 Watts so you don't have to revisit this area.

2. Power supply connections.

Most P4 motherboards require the AT12V connection from the power supply. A machine made during P3 days will not have this connection.

3. RAM.

Doubtful you can recycle your RAM. Most P3's used SDRAM, today's P4s take DDRAM.

4. Case issues.

Some machines took a custom approach. Since I can get a 400 or more Watt PSU with a case for the same price as just the PSU most places, I'd just forget recycling those parts.

Hope this helps.