Several things come to mind.
How much memory in the computer?\laptop ?, if you attached the monitor to the back of it?
Do you have a video card with memory[the card will show banks of memory chips].
Usually, if you don't have enought memory on the computer, the more u use [getting on the internet, going to more then one site,etc.etc] the less is for your monitor.The CPU will Keep the monitor alive, but it is NOT the mose important thing.
If you can put the Dell Vaio on another computer, even in the back of a laptop. If the u have the same problem, the monitor is going bad.Maybe one or all the output transistors, sometimes the small video driver transistors that feed the outputs.