recording from desktop to set top with built in dvr

Please move as needed. I am using a desktop computer with a vga to tv converter to connect to the tv line in in order to display the computer screen onto the tv. The set top box connects the co ax line out to the boxes rf line in. This allows the tv to display whatever channel is selected. The set top output is a hdmi connection. Is there a way to connect the vga out to the set top in in order to use the dvr function? In the past I used a computer connection to a vcr to a dvd recorder. Is a similar connection possible? I decided I did not want to create so many dvd's. The dvr can store the content without physical media.