No, the old XP wont run on the new computer . Even if it did its considered piracy as you don't have the right to NORMALLY transfer licenses from computers( exceptions do exist , but you need to have the original XP installation CD , and reactivate it with tech support on the new machine ) .
The easiest thing to do is to just buy a full version of Windows 7 and install that on your new PC .
Plus you can't upgrade a 32-bit installation to 64bit , and your new PC PROBABLY has more then 4 gb of ram( or you at least want to option to upgrade this latter ).
PS : Home Premium does most of the same stuff as Professional windows, and you can buy Home Premium FULL for about 100$-maybe a bit more . I added this since I assume your trying to save money .