Your link just went to the Newegg home page for me. Is this your PC?
http://www.newegg.com/Product/Product.aspx?Item=N82E16883103924&cm_re=ATC-605-UB11-_-83-103-924-_-Product
If so, can you read the nameplate on the PSU? We need to know the amperage and wattage of the +12V rail(s) if you want to use the same PSU.
If you would rather upgrade the PSU to use a faster card, please state a total budget for card and PSU.
Looking at the pic of that open case on the website, it appears that the HDD mounted in the drive bay will limit you in the card's length. Measure the distance you have from the expansion slot cover to the HDD. That will be the max length card you can use.