Whilst it's not the best way to power the card, using an adapter should work fine in terms of power. If you're getting nothing on the screen that could be due to a number of issues. Try removing the GPU and plugging the video cable into one of the motherboard outputs if your cpu has integrated graphics (most modern cpu's do). If the display works then we can be pretty sure it's an issue with the card. If not then we need to look at other options.
Maybe also list your system specs - it's always helpful information for us to have.