If your XP Professional disk is NOT an "upgrade" install, then you should be able to install it just like you would normally. You should have an OEM license key as well. Also, if you received the WinXP with your laptop, you might run into issues if you try to install it on another machine. Mainly, MS may block online activation if the license key is used multiple times (ie your laptop is running the same license key already). Since you say your desktop is running windows 98, I'd be weary of installing XP on it. Does it have at least 256mb of RAM and a fast processor?
To check if you can launch the XP installation you can try to boot from CD (check your BIOS boot-sequence to make sure your CD-ROM is read before the primary drive). If it brings you to the installation screen, you will probably be able to install XP. However, what I said about license keys still holds true. The installation will only ask you for the key AFTER formatting your drive....so you'd be SOL if it is rejected or unable to activate online. HTH