My moniter is hooked up, but not running...Why?

Today I was moving from an old office and was trying to hook up my moniter to my computer. The computer was fine and it started without a problem, but the moniter stayed black. It flashed a brief "no signal" message, but then the power on began blinking and turned orange and then my moniter went black. I have no idea how to fix it and know nothing about video cards or hard drives or any of that. But what I do know apparently isn't enough. I have tried many moniters on the same computer, all of them (working previous to this problem) had the same thing happen. My computer is a Vaio PCV-C41L and my moniter is a flatscreen HP HSTND-2L05 ( I got those off the back of each one, they were under model number). Please help: I need important files that are on that computer!! (I am using the only computer I haven't dismanteled.)