I'm going to assume your HDD's are connected with IDE. Take your old HDD out of the case and put it in your new PC. You will need to set the jumpers accordingly to master/slave. The HDD's should have a label on them that tells you how to do this. Make your new computer's HDD the master and your old one's the slave. Since your old HDD is already formatted and partitioned, boot up the PC and enter the BIOS and make sure the HDD's settings are ok. Then boot XP and it should show up. Then transfer files.
If both are SATA, which I doubt, just plug them in
If one is SATA and the other is IDE, set the IDE on master and have the SATA plugged in.
If this doesn't work, let us know.