You've got a Genie Lite H44 receiver.
I swiped a picture of the back from the Solid Signal website. If you look at the group of three connectors in the middle, from left to right they are A/V Out, Coax Digital Audio Out, and HDMI.
The A/V out connector is DirecTV's composite output connection, which can supply either composite video and left and right audio, using a cable like this one
http://www.solidsignal.com/pview.asp?p=10PINCOMPOS&ss=534051 or component video with a cable like this one
http://www.solidsignal.com/pview.asp?p=H2510PIN. I suspect you're using the former.
If that's the case, you don't have to worry about the surround signal, because all you're getting from the A/V out on the Genie Lite is standard 2-channel stereo.
You say your surround system is pretty old. I suspect that you also have a regular old standard definition TV, since you're not using the HDMI output from the Genie Lite.
How you proceed depends on whether or not your TV has audio out jacks or not.
If yes, then you need a stereo RCA PATCH cable, which has two male connectors on each end, one red and one white. You connect the two audio outputs from the TV to the two audio inputs on your surround system.
If no, then you need a stereo RCA EXTENSION cable, which has two female connectors on one end and two male connectors on the other and uses the same red/white color code. You unplug the audio connections from your TV and connect the female ends of the extension cable to those, then connect the other, male ends to your surround system.
If you have other connectors besides the red and white RCA L/R jacks on your surround sound system, you may be able to get better sound depending on what connectors are available, but you might have to buy a coaxial digital sound converter (there are a few different types) and different cables.
If you want more help, post your TV's model number (or a picture of the back) and a picture of the inputs for your surround system.
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