Your problem has nothing to do with 4k.
Your HTS doesn't have HDMI-ARC so you can't use the HDMI cable that plays the DVD on the TV to get sound from the TV to the HTS. ARC only works when both the TV and HTS have it and both are configured correctly.
The HTS only has analog audio inputs so you can connect the headphone out of the TV to the HTS. You just need a cable with a stereo 3.5mm plug at the TV end a 2 RCA plugs at the HTS end. Select a surround mode like Dolby Prologic that is designed for a stereo input. Not digital surround but no way around this without getting a new HTS.