I do not believe the Radeon card is your problem if I understand what happened. After you installed the operating system, you can not or have not installed any other drivers or software to Win98. If that is true then Windows has generic VGA drivers installed for the video card and does not know what kind of card is installed. This will be the case until you put the drivers for the card into the system. The first thing you have to install after Win98 is done booting from the install is the Via 4in1 drivers. If you do not do that all kinds of weird problems pop up.
I would start over with formatting the disk and installing Win98 over. The other thing is just have the bare minium hardware installed; hard drive, memory, video card. Disable any on-board stuff so Win98 only has to deal with the basics. Win98 can get confused if you throw to much stuff at it all a once, I have done that before. After it is running with the minium installed and Win98 is up then install the Via 4in1 drivers. By doing it this way, if the problem is still there, it will be easier to trouble shoot. Install additional hardware one thing at a time with rebooting Windows between each hardware install. Slow down and take it step by step. Something else I have had happen was a bad new CD-ROM. It would misread files on the install. I had to try a different CD-ROM just to copy the setup files from the CD to the hard drive. Then I ran the Win98 setup from the hard drive, which goes much faster. It took me awhile but after trying 4 times to install the system from the CD, then trying to copy the setup file to the hard drive, did I find the bad CD-ROM.. Good luck to you, you will be able to figure it if you go step by step and break it down to find the problem.