I've seen troubles with the XP Upgrade (of whatever SP) accepting the validity of those gawd-awful restore disks of a lot of the big OEMs. I've heard that an upgrade version of XP will install if the targetted machine is actively running its old version - in other words, it will upgrade over top of its older self even when that was an OEM version in its original creation. But that has its own set of issues, that often any absurdities that have crept into the old version after all those years will be transferred straight through to the new installation. That's why I always do a clean install on a newly reformatted (or brand new) blank disk.
But in my own practice, when I have to do an upgrade on one of these OEM monsters, I first assure myself of the validity of the original license, reformat, and then slip in my own true-blue MS Windows '9x original hologram CD to satisfy the XP installer. At that point, the customer can have the old Gateway disks back and hang them on the rearview mirror for all anybody cares.
In your case, you may need to stumble the long way around the barn. If the XP install disk won't accept your original restore disk when you attempt to clean install on your new drive, you might try this somewhat complicated work around.
Open your machine and put the old disk back in, as master on the boot channel. Put your new disk in as slave. Do what ever you need to about the optical drives, and boot up into the old Win98 operating system. Put the new XP CD in the drawer and let it start its routine. When it reaches the point of asking if you want to upgrade the version of Windows it found in C:\Windows or do you want to install a new copy somewhere else, force the installer to go to the new physical drive. You'll have to partition and format as part of the first step, but your old drive should remain untouched. However, you need to be very very very careful that you are absolutely sure you've gotten the installer oriented to the new disk and not the old disk. Otherwise everything on the old disk will be toasted. Once you get XP install on the new disk, you can simply rearrange the master/slave relationship of the physical disks on the IDE controller (change jumpers, cable select, whatever) and boot XP on the new disk. The old disk will simply be the next drive as plain storage - with, can you believe it, all you old data right where it has always been except now it's on D. None of your old programs will work, but you already know that.
As for all the mixed up drive lettering of the optical drives after all this swapping around, you can go into the system administration properties and manually reassign the drive letters of any logical device. Yeah, it would be nice to be able to set all that up the way you want before/during the install, but the shortcoming is recoverable. Don't sweat the little things.
As for that service pack disk... it will only upDATE your operating system, it will not upGRADE it. Use it after you get XP running for an easier patch to SP2 rather than dealing with downloading it all from WindowsUpdate. But after you patch with the CD, be sure to go back to WindowsUpdate and retrieve anything newer since that CD was produced.