may be code below will help you:
QProcess *process = new QProcess(this);
QString program = "explorer.exe";
QString folder = "C:";
process->start(program, QStringList() << folder);
I think you are trying to execute program that doesn't consists in global $PATH windows variable, that's why winword.exe doesn't executes.
Also you may need to define absolute path to program, e.g.:
QString wordPath = "C:\Program Files\Microsoft Office\Office12\WINWORD.EXE"
process->start(wordPath, QStringList() << "");
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