Thanks for your reply, Raziel.
I had already disabled all that stuff.
As it turns out, upon reinstalling the program, I saw that it was necessary to install Visual C++ to make it run correctly.
Previously, I had unwittingly uninstalled Visual C++ through Add & Remove Programs, when cleaning up my computers for better performance.
So... now Ad-Aware is working like it should... it has not popped up unexpectedly again.
Paula