Remember the system tray icon isn't the physical protection, just the interface to the settings and functions, etc. Check the task manager and see that avast is running, with the exception of the ashDisp.exe the icon function, you should have ashServ.exe, the main scanning engine, ashMaiSv.exe, the email scanner (only if you actually have it enabled), ashWebSv.exe the web shield and finally the aswUpdSv.exe the avast update service.
So there is no need to break into a sweat just because it isn't there confirm avast is running before breaking into a lather.
There really shouldn't be a need to reinstall at the drop of a hat there are other options that you should do first, especially with dial-up and a 27MB download. If your downloaded file is much different then it could well be a failed download and from what you say it looks like that.
So you should follow the procedures as laid out in my first reply, none of which require you to download, if all else failed then we would consider a clean reinstall. However, it depends on why it happened in the first place, if it were another program responsible then a reinstall may simply have the same happen again.
So start from square one, read my first reply try what is suggested and answer the questions asked and we can start from there.