Have a Menu Problem, too
When mouse_sync is off the cursor isn`t visible over the added menu.
But when mouse_sync is on the cursor allways blinks.
(32 x 32) cursor image, tga

For your Problem:
Look at the mci.c example, there is a menu code
Copy it in an own Project (without WinMain and LRES stuff) and try.
Worked very well for me