Monitors LCD monitor with both DVI & VGA connected ... doesn't work ?

[PoBoy]

I have a Sam 2033sw+. Using it with DVI only till now. The CRT I used with my downloading rig died. Yest I thought why not connect it to the VGA port on the monitor - as long as I used only one of them it would be OK. With my main rig switched off, the d/l rig worked OK thru the VGA port. With the d/l rig switched off, I do not get a display from my main rig thru DVI.
Is this normal ?