DirectInput ignores keys, because a window that is not foreground cannot acquire the device

Symptoms

Keys or the mouse do nothing in the game, though the window shows. WINEDEBUG=+dinput reports that the window is not foreground. Calls may return DIERR_NOTACQUIRED or DIERR_INPUTLOST.

Cause

A DirectInput device set to foreground cooperation (DISCL_FOREGROUND) can be acquired only while its window is the foreground window. A window started from a script, or behind another program, is not.

What to do

Bring the game's window to the foreground before you send input. Then wait a moment, so the game can acquire the device again. Inside Wine, a helper that brings the window forward and then sends input with SendInput does both (input inside Wine). In POD this helped only in part (observed).