It's unlikely that the card needs its own power supply, it's only the really high end cards that need to draw more power then the PCI/PC Express socket can supply.
This may sound a little obvious, but are you sure the monitor is plugged in to the right socket on the card eg, the VGA or DVI socket and not one elsewhere that may be on the back of the PC thats for onboard graphics.
Try making sure the card is fully clicked in to place, sometimes you need to push quite hard to make it connect.