I'm afraid you simply cannot run 3 monitors on that setup, especially not for gaming. Your video card (the Nvidia GT 520) will probably support 2 monitors, but definitely not 3. It MIGHT be possible to use the integrated video outputs (on the motherboard) simultaneously with the Nvidia video card to output to 3 monitors at the same time, but you will not be able to run games on that configuration, and I would not be able to help you to achieve that, if it is even possible.
A possible solution would be to upgrade the video card, as you asked first. You would then be able to output to 3 monitors simultaneously, but your computer is much too old to be able to play any demanding game on 3 monitors simultaneously. Moreover, with a 200$ budget, the best video card you could buy would be the one I cited, which would only BARELY be able to achieve playable framerates on recent games using multiple monitors.
So, to answer your question, I do not think you can run 3 monitors using both the integrated card and your Nvidia GT 520. Even if it was possible, you will not be able to play any games on this setup. I hope this answer your questions, even if it does not help you.