Product Key attached with a software from Microsoft Windows Operating system.

OEM Windows discs, whether from Dell or from Microsoft, are only legally licensed for the computer it was delivered and installed on.  The IP address has nothing to do with it.  

I had a Desktop preloaded with Windows XP Professional Pack1 operating system. Thereafter, I donated the desktop to a School nearby and bought the DELL Dimension E520 Desktop with Windows Vista pack2.  I still have the CD of Windows XP professional pack1 (a Licensed copy) with me. Now I have planned  to partition my Harddisk in Windows Vista in C: and D:  Currently Vista is loaded in C:\ . And I want to  install  the XP Professional in the Drive  D:\. But the question is - should I install  the Windows professional XP from CD (licensed version of pack1 Home edution) in D:\  will it create a problem with the Desktop donated by me to the School - because I fear the IP Address of my Desktop (E520) is different from the IP Address of the School ---again,  the PRODUCT KEY of Windows XP Professional pack1 Home Edition might have two different IP Address recorded  " My Desktop E-520 and with that of my previous Desktop donated and working  with the School  ! Please suggest me in this matter. BASAB ROY.

You should have given the disc to the school when you gave them your system, as they might need it to reinstall their OS.:emotion-14:

Technically you can install it without effecting the other computers as Dell XP Reinstallation Discs unlock when a Dell BIOs is detected...

Legally you can't because you have a Home license and not a Professional/Ultimate license so are not eligible to exercise downgrade rights. Also with downgrade rights you are not allowed to dual boot, i.e. only 1 Microsoft OS at a time can be installed unless you purchase an additional license.