Hi Jen
avast! is a top-notch program, and I recommend it for computers running Xp or newer. But it's too much for most older Win9x systems. avast! starts several background processes, and the load can simply be too much for older systems with less than 256mb of memory. The Win9x series of Windows also has trouble with heavy multi-tasking - due to it's poor handling of 'system resources'.
You can try a simpler program such as A-squared Free, which still supports Windows 98 ---
http://www.download.com/A-squared-Fr...dlPid=10832180
I used to recommend AVG for Win98, but they've stopped supporting Win98 with the release of AVG version 8 (as you've discovered). The well is starting to run dry for Win98 support from antimalware vendors, especially for free versions.
You shouldn't have too much trouble uninstalling avast! and trying a-squared.
Best of luck
. . . Gary