Miguel_T, You should be fine using the disk on the other computer. I don't think you will have any issues. You can use the product key from the disk you use to install  on the computer.
I have 2 Inspiron 8600 notebook computers.  1 purchased from Dell refurbished call it computer "A" and the other was purchased from Dell new call it computer "B".  The systems are identical save minor software differences.  I want to do a repair reinstallation on computer "A" ...however the CD's for computer "A" are in storage.  I do have the CD packet from computer "B" ... the new 8600 that includes the Reinstallation CD.  I have product keys for both "A" and "B" ... can I use the XP Pro Reinstall CD from computer "B" on Computer "A" for the reinstallation/repair?  If prompted, which product key should I use?  I wasn't sure if the CD's were somehow unit specific.  Thanks very much ... Col T. 
Can I utilize Re-installation CD from 1 Inspiron 8600 to my other 8600