You dont have to "back up" the photos using a backup program, you could just COPY the photos from your computer hard disk to another medium.
Now I know Windows 98 did not support all the latest technology, but some of your options are:
Buy a USB Memory stick and copy the photos to that (if your PC has a USB slot)
If your PC has a CD writer copy the photos to CD.
If you know someone who is fairly technical they could take the hard disk out the PC case, put it in an empty hard disk caddy, plug the hard disk caddy into a new PC and copy the pictures on to the new PC. (I have a PC caddy that could do this and it would probably take me no more than 30 minutes)
So you DONT need to lose the photos as it should be fairly easy to ge the photos off if you have the right technology.