First, why are you changing from HDMI to DVI on the same computer/monitor? You should only have one connection between the 2 of them at a time.
This sounds like your GPU (video card) assumes you have 2 monitors attached to it and it extends the desktop to the second monitor, only there isn't a second monitor. The icons are there, just not on the second monitor. I know this sounds confusing.
Just remove one of the connections and you will be fine. Good luck!!!