All it says is that you have a 300W PSU (the first link that you provide didn't even include that info); you have to remove the side panel and check for the cable or provide the make and model number of the included PSU. As you can see at
http://www.realhardtechx.com/index_archivos/Page362.htm the recommended PSU for a GTX 960 is 80W more than a R7 240 (that matches the expected additional power draw). If I were you I'd presume that a new quality 400W PSU is required.
If you read the reviews, is this correct? "-If you want to install a video card that is 2 slots wide there may not be room for your sound card and other components because the PCB setup." You have the PC; therefore you can easily check it.