Should I worry about this about my first iMac

I own several apple products including iphone, ipod, ipad, and macbook pro. But this is my very first iMac and it arrived yesterday (refurbished 27 imac 2011 from apple store).I am excited, but the first set up was not smooth. After I pressed the power button, I heard a tone, but the screen was totally black. I waited for about a minute, still nothing showed up. I tired to turn it off and on again. It didnt work. If I typed in the keyboard or move the mouse, I could hear those sounds from the speaker indicating that I was navigating through the set up options, but the screen was black. After aobut 20 minutes, I started to be panic and dialed the apple care number. As I was trying to reach a technician over the phone, the screen suddenly lit up. Ever since then, everyting seems normal. I have installed software, created boot camp disk, install windows, surfing internet. Everything is quite nice so far. But I still could not help wondering what the problem was when first trying to set up the imac. Anyone has a clue or heard something like this before? Thanks.