If you look at the video card you can see if you have multiple ports , you would need to see what ports you have . Do you have a DVI and a HDMI or do you have a VGA and DVI , if you have two ports and the two monitors have those ports then you can connect. Depending on the model of video card will determine what you can do with connecting two monitors. Your computer has been discontinued by HP so that means it's on the older side and you may need a video card upgrade for this to work. So if you can you need to post the brand and model of your video card.
The card has only a DVI and HDMI output so I know I need a new card. my problem is the PSU is only 250 and all the cards I've seen require at least 300. I'm just wondering if a 250 card with with two outputs is available.
This link is a graphics chart that lists the video cards in order of top quality to the lowest and it's for each brand Nvidia and AMD/Radeon.
So you do have some ptions and it's going to depend on what you want to spend.
You can upgrade the video card and it may mean an upgrade of the psu as well.
Since your not gaming with the card I do think you can use the card that you have and all you need are a couple of adaptors.