Morning start-up of monitor takes a long time. "Analog" appears at top left, then picture goes off. After turning monitor off-on many times, monitor eventually stays on and works fine the rest of the day.

This is usually caused by the video card doens't have enough power or is degraded, the video cable is bad/poor.
Connect the monitor to another computer and verify that it isn't the monitor. If so, confirm that it is the monitor. Otherwise it is the video card.
If it is embedded video card, purchase/borrow another video card and install it. If you don't replace the card, you will have to disable the embedded video for the video card to work.