The free trials for Adobe Photoshop (
http://www.adobe.com/products/photoshop/tryout.html) and Jasc Paintshop Pro (
http://www.corel.com/servlet/Satellite?pagename=Corel3/Downloads/Trials) seem to be only for XP and 2000. You could try looking for older versions.
Paint.NET (
http://www.eecs.wsu.edu/paint.net/download.html) is free, but claims to only work on 2000 and XP. You could try it anyway.
You could try The Gimp, which is free and claims to be able to run on Windows 98 (
http://gimp-win.sourceforge.net/stable.html). However, it's likely a bit harder to install.