Is it possible to completely copy a HARD drive, OS and all from one computer to ANOTHER and make it a second drive on the new computer?  Copy HP hd with win 98se to compaq hd with winxp.It is possible, using a program such as Norton Ghost or Acronis TrueImage.
This will copy everything though, so is not really recommended for moving an entire PC - you'll have DRIVER problems at the very least.
I'm sure someone else can fill you in on the problems you'll face.
Ghost and TrueImage are more for moving between hard disks, not PCs.
To move between PCs, use a backup program to backup everything you want and use the Files and Settings transfer Wizard in XP to copy settings over, unsure if there's an equivalent for 98.Windows 98 needs to be on the primary partition of the first (master) hard drive. XP can be installed afterward to the other drive.

Your method proposed is full of other reasons it won't work as well.skylane42, do you want to create a dual-boot configuration, allowing you to run either Win 98SE or Win XP?  Or, do you just want to move the hard drive over to the other computer for more hard drive space in that computer?  I think this point needs clarification?

I'm also think your message is not clear on whether you really want to physically remove the hard drive from one computer and put it in the other.  You say copy from the old hard drive to make a second hard drive in the new computer.  Doesn't quite make sense, in my opinion.  Exactly what do you mean?The dual boot would work.  That way I could use either OS.  I have reformatted the Compaq from a blanked harddrive.  I bought a set of recovery cds.   The problem is that the programs are not all there.  Stuff LIKE MS word and works do not reinstall.  SO ..I thought that if I could get my old HP recovery disk on the Compaq then the programs would be back and I could use the better computer.You will not be able to reinstall software from one set of recovery CD's onto a totally different machine than they were DESIGNED for.