I have the same issue. I've been running Avast for many years, never had an install issue. I just reinstalled Win 8.1(64) after trying win10 for a few weeks, it was a clean install so there shouldn't be any leftovers.
One of the first things I did was DL and install avast_free_antivirus_setup_online.exe
It seemed to install without any issue. There is no tray icon or any icon in the APPS window. The only proof that Avast is installed is the Avast service in taskman.
Yes, I have all toolbar icons showing and active, so it's not hidden.
I have done all updates, rebooted, un/re installed Avast and have the same issue.
Win 8.1, RAM 16GB, Intel i7-5930K 3.5GHz
Nvidia Geforce GTX 1080
Thanks