adding a new card has many reasons. One being for most people is that their current card (and especially with integrated video) has limitations. The other is that they have a problem with their current one...
If you do doubt that buying a new one will help your situation, maybe try and borrow a card from a friend, or buy a cheap one to test the theory...
There's also the cable and monitor you should test out as well, if the video card isn't to blame.
If you plug in a speaker and press the power button, do you get any beeps or other signs?