First, although your TV connects with HDMI, it is unlikely that it will get any multichannel signals unless it has its own multichannel amp/speakers built in. The EDID handshake between the TV and the sources will tell the sources to send only stereo.
Second, regardless of what the TV is getting, it will probably output only plain old DD in stereo.
Third, I do not know of any modern (HDMI in/out, HD codecs, etc.) standalone processor in that price range. However, you can buy an AVR with preamp outputs for this purpose and ignore the amps. Remember to connect the sources to this AVR and not directly to the TV in order to assure getting the HD codecs in multichannel.