Does Sony Blue-ray BDP-S350 output HD audio from ?

Looks like it is only through HDMI. The unit does have 2 channel analog output. You need 7 channel output to get the Dolby TrueHD for all channels.

If you bought a BRP that did have 7 audio outputs, you could connect it to your older receiver's analog inputs to get the TrueHD sound. Then use the HDMI just for video connected to your HDTV.

The Panasonic DMP-BD50 looks to be your best bet for what you want to do.

The new Sony BDP-550, coming out in October, will decode TrueHD internally and output through the analog jacks.
I am thinking of purchasing this one so I can use my Anthem AVM20.

My question is this does the de-coded HD audio signal come out from the coaxial / optical or analog outputs or only hdmi ?

Just to set this straight, the new lossless surround codecs CAN'T be transmitted via coax or Toslink, ever, period. The SP/DIF connection (coax or Toslink) can't handle the bandwidth requirements of a lossless 7.1 channel datastream. That's why the SP/DIF output of an HD DVD or Blu-ray player outputs a downconvert in DTS format of the hi-rez soundtrack.

Lossless 7.1 ch. digital datastreams from the HD DVD and Blu-ray codecs (and SACD surround, for that matter) require HDMI. They need those extra conductors to transmit all those extra channels without lossy compression.