How can I install QtWebEngine on Ubuntu
This is specific to Ethereum and the ethereum-qt PPA, which was being upgraded from Qt 5.4.0 to 5.4.1, something that takes many hours to complete. Just apt-get update && apt-get upgrade and everything should be fixed.
I found that another cause of this 'module "Qt*" is not installed' class of problems on Ubuntu at least is the environment variable LD_LIBRARY_PATH not being set. It should include the path to the lib directory of your Qt installation, e.g.
if [ "x$LD_LIBRARY_PATH" = "x" ]; then export LD_LIBRARY_PATH=/home/username/Qt5.4.1/5.4/gcc_64/libelse export LD_LIBRARY_PATH=/home/username/Qt5.4.1/5.4/gcc_64/lib:$LD_LIBRARY_PATHfi