Yes, you would need to replace the RAM too and you'll probably want a faster hard drive and perhaps a DVD+-RW.
Building a computer yourself it relatively easy.
Here is something you could get on the cheap:
-----------------------------------------------------------------------------------
BIOSTAR IDEQ 210VB AMD Socket A(462) Barebone - Retail - $165.00
http://www.newegg.com/Product/Product.asp?Item=N82E16856115017
-----------------------------------------------------------------------------------
AMD Athlon XP 2600+ Barton 333MHz FSB Socket A Processor Model AXDA2600DKV4D - OEM - $74.99
http://www.newegg.com/Product/Product.asp?Item=N82E16819103417
-----------------------------------------------------------------------------------
Kingston ValueRAM 512MB 184-Pin DDR SDRAM DDR 400 (PC 3200) Unbuffered System Memory Model KVR400X64C3A/512 - Retail - $43.12
http://www.newegg.com/Product/Product.asp?Item=N82E16820141424
-----------------------------------------------------------------------------------
SAMSUNG SpinPoint P Series SP0411N 40GB 7200 RPM IDE Ultra ATA133 Hard Drive - OEM - $48.00
http://www.newegg.com/Product/Product.asp?Item=N82E16822152008
-----------------------------------------------------------------------------------
SONY Black IDE DVD Burner Model DWQ28A - OEM - $38.99
http://www.newegg.com/Product/Product.asp?Item=N82E16827131256
-----------------------------------------------------------------------------------
Total: $370.10
You could actually reduce this price considerably if you opt for a regular old mid-tower, but micro-atx cases are so much nicer.
I'm going to assume your not much of a gamer because you still use a 900 Mhz machine. If you want to play the lastest games you could get a NV geforceFX and a SB Audigy, but the motherboard that comes with the biostar barebones kit has built-in video and sound.