What kind of cable do I need

Pal you have something I've not seen on an audio component.
A "LAN" connector is typically an RJ-45 8-pin style which is normally a balanced connection. You'll need to get the pinout from the manufacturer first. Then you may need to build your own cable. Does your DAC have a balanced input is the next thing you need to know, and what's the connector type? A Cannon plug (a.k.a XLR) uses pins 2 and 3 I believe for a balanced input.

The LAN connection uses an ethernet cable for broadband hookup to a computer.Read your manual,it contains lots of useful info.

Do you mean the DMP-BD35K? According to Panasonic's website, this and the other network connection are for BD-Live compatible devices and allow you to connect your player to both the internet (to obtain BD-Live info, firmware updates, etc...) as well as sharing your player content/output to other devices on your home network (if you believe all the marketing sheets and manual say).

For analog 7.1 ch output (after the Panasonic decodes) the player has straight 7.1 RCA analog outputs for connection to your pre-amp or receiver.

For Digital outputs, it states it has TOS-Link (fiber optic) and Coaxial (S/PDIF) connectors as well as HDMI
output for best-quality output to your surround processor and/or DAC.