Hi Merrikingfis,
I understand that you need to install your original operating system which you have purchased on your old machine.
Please follow the below steps:
1. Please backup your important files to any other ext. Hard disk or DVD disk. During reinstallation of your operating system, usually your data wont be get lost but for safer side its good to go for a backup.
2. Put your windows original CD into your cd drive. An autorun window will appear. Click on Install option.
3. The new installation will automatically detect the previous windows installation (pirated installation) and provides you with the options for 1.Installing fresh copy 2. upgrading the existing installation.

4. Choose upgrading option as this will overwrite the pirated windows version with the new original windows.
5. You system may restart several times during the process.
6. Provide the prompted informations during the installation.
7. When prompted the windows original serial key, provide the one which came with your original windows CD (Usually written on the windows CD pack)
8. Thats all, your system is now reinstalled successfully with your original product key.

Please follow the above steps and let me know your doubts in following these steps. if you encounter any problem, please provide those problem back in comments section in detail as that will be useful for me to assist you to solve those problem.
Thanks

To do that you do not need to remove the old one ...if your installer(the new one ) is on a boo-table cd ...just go to bios to select the boot order from the advanced features...to boot first from cd ..and second from the Hdd...after that insert the cd and restart ...it will prompt you to press any key to boot from CD ...
at this point you started the installation ...after loading primary files...it will ask for the agreement ..and after that will look for previous installations..(operating systems) it will find the other one on the C drive ...and at this point click D to delete the partition ..L to confirl ...C to create a new one from the raw space created...and after that enter to install ...It will prompt you to format the partition ...choose the NTFS quick ...will format and start loading files from cd ...
After finishing the load..it will restart and begin the actual install of the windows xp...do not press any key on second restart cause it will reload from the beginning...just let it boot and continue with the installation ...During the installation it will ask to enter the product key ..and to choose the region and time ...and the way you connect ...just click typical and deal with the network after finishing the installation ...
anyway ..I will link you here to a site where you can download and print the steps one by one to have the papers in hand if you forget something ...
Good luck and ask me anything before you begin if you do not understood the procedure...
http://www.microsoft.com/windowsxp/using/setup/winxp/install.mspx
Here are the same steps I explained but with illustrations for better understanding ...
if you have the possibility print them to have 'em on handy ..
Good Luck !
if you want also you can download this simulation to make a few steps and get familiar with http://www.download3k.com/DownloadLink1-Windows-XP-Setup-Simulator.html
beware it is a direct download..