The Gateway Solo notebook series has been around quite a long time - early models ran original Pentium processors (as in the 133mhz to 233mhz variety).
If the old Solo can boot from a CD, you can test its hard drive, memory, & processor by starting the Solo with a "UBCD" (Ultimate Boot CD). This will let you know if the old Solo's parts are defying time & continuing to operate in good working order (truthfully, they are well into their golden years).
From another computer in good working order, download the ".iso" image for the "Ultimate Boot CD" & use a CD-burning program such as Roxio or Nero to burn the bootable image onto a CD-R. You'll need to use the "Burn an Image to Disk" option when burning the disk, as simply copying the file to the CD will not result in a bootable CD. Full instructions are on the website --- http://www.ultimatebootcd.com
It may be that the CD drive in the Solo is faulty. You can try taking the hard drive out & use an external 2.5" IDE-to-USB adapter to connect it to another working PC, and then copy the Win98 CD's files directly onto a folder on the Solo's hard drive. Then place the Solo's hard drive back in the notebook case, use a bootable floppy diskette to start the Solo into the DOS command prompt, and from the command prompt start Setup. If you are lucky enough to try this method & need more details, let us know.
It will be a testament to Gateway's selection of quality parts & the Solo's past owners if the laptop is still in good working order.
Best of luck
. . . Gary