It must be there, if you have the Internet Mail provider running you will see
ashMaiSv.exe file there. If you have nothing, something is wrong in your installation. I'm not sure now, but I think
ashDisp.exe (that is the application which 'generates' the icon on system tray) does not 'run' this way into Windows98 (just in XP).
As you can see, please, uninstall and install avast again:
1. Download the avast! setup (current version 4.1.319). Take note of your Registration key or, if you need another key, the registration form can be found
here2. Desinstall avast (Control Panel)
3. Boot
4. Use
Avast Uninstall for complete desinstallation
5. Boot
6. Install the downloaded setup file
7. Boot
8. Enter the Registration key and configure avast! for your needs