Frequently asked questions: try this thread first

Dorico not starting on Windows 7 with message "Audio Engine Process Died

Although it is not officially supported, Dorico should also run fine on Windows 7.

If you are on Windows 7 and Dorico hangs during start-up with the error message “Audio Engine Process Died” then chances are high that you are missing a certain Windows update.
Please download and execute Platform update for Windows 7 SP1 and Windows Server 2008 R2 SP1 - Microsoft Support and then reboot your machine.

Besides that Windows update, you also must have Windows Aero enabled, then Dorico shall just run fine on Windows 7.
Here a link that explains how to enable Aero: How to Turn On and Enable Aero in Windows 7 (Enable Aero Peek) « My Digital Life
For how to enable Aero on Windows 7 Home Basic read the advice from user ShikiSuen: Win7 users MUST READ: Enable Windows Aero and Install KB 2670838. - Dorico - Steinberg Forums