Pioneer PDP-436 Plasma: I have lost one channel of sound at the speakers and the line output but have both in the headphones.

Check whether the audio is muted by accidental press at remote control button. Enter its sound menu, and check it. If muted, as you know there will be no audio output. If not muted, check the speaker/s. If found OK; check and replace the damaged component/s at its audio output section circuit board. If needy, replace this board as card basis. If you wish to get some details; check the site linked here. Surf the site with patience. Pull up older posts. Surf the site with patience.
http://electronicshelponline.blogspot.com/

This model has no headphone out put. In the rear panel there are two monitor audio outputs which could drive headphones, but I think the volume output to a possible monitor matches the tv loudspeaker output, and may not turn off the audio separately.

Pioneer plasma pdp 436 xde cannot connect external speakers has telly no sound keff system surround we had packed up and now trying to connect some other speakers any help please

Refer its user manual for details. There should be a facility to most of Pioneer sets.

Does the set have sound with a DVD etc. directly connected to one of the audio/video inputs this set has?

it comes with 2 26 watt speakers and digital surround sound :)

Sounds like the speakers are cracked (no pun intended) - damaged cones. Connect external speakers or connect a headphone to the headphone jack to see if you get the same sound. If not, then the speakers themselves are damaged.

I checked on Pioneer's site and couldn't find literature for this model, but did find the product information sheet for a model PDP-614MX. It may be similar, but no promises. This model has no audio output available, but does accept several audio inputs. It shows speaker terminals on the bottom and claims a 9-watt output for each channel. Speakers that mounted on the sides were available as an option.

This monster was originally designed for professional use (stores and such) as strictly an output display device. Probably the best solution would be to use this to display the video, and run the audio output from the source (DVD, satellite receiver, etc.) to a separate amplifier to drive your speakers.

maybe in your cable box