You're leaving out details. What port is the new card going to be using? In most cases a new card will disable the on-board video port, but you seem to still be using it, so it never got disabled. In the bios, revisit and be sure that whatever relates to video is proper. This varies so follow what HP(support website) provides in their adding video card instructions. Further, you new video card should have instructions as well. While you state your current PSU is enough to power the new card, just what are the specs needed. You need to play it well above the wanted specs in order to deliver on a constant basis. If the new video card wants 300W, be sure your PSU is at 400W or better, yours is 300W. Though it may work, typical video power issues arise after 30-days or so, because you're pushing the PSU too much. Are you sure you added or connected the extra power leads to the video card from the PSU? Understand the video card WANTS 300W, what about the other devices? It cuts it close.
Video manager s/w from the card maker provides direct access to its features. I hope you installed all new s/w and drivers fully and you can access it. You need to tweak it but also select it. No display, then verify is other than VGA, you select from the monitor itself(OSD menu) what video port you use if applicable. Then at the PC use the video manager to get it all settled. No shortcuts, please check and verify. There are YouTube videos if you want to review them, sometimes it helps.