Right Front and rear speaker do not work proberly.

Try resetting it:
Link to Manual

take one of the front speakers out and pull out the head unit and unplug a set of audio wires(front right, front left ect.) and hook it up directly from the radio to the speaker there for bypassing all the cars wires. If it works then there's a problem with the car's wiring(maybe an inline amp). If it doesn't work, then try a known good speaker from somewhere else(home stereo speaker for example) and connect it to the radio, if the speaker works, your radio is fine and there may be a problem with the speakers. If it doesn't work then you have a problem with the head unit.

2003 Hyundai Elantra Car Stereo Radio Wiring Diagram
Radio Constant 12V+ Wire: Red
Radio Switched 12V+ Wire: Yellow
Radio Ground Wire: Black
Radio Illumination Wire: Pink
Radio Dimmer Wire: N/A
Radio Power Antenna Trigger Wire: Gray/Orange
Radio Amplifier Turn On Trigger Wire: N/A
Front Speakers Size: N/A
Front Speakers Location: N/A
Left Front Speaker Wire (+): White
Left Front Speaker Wire (-): Brown
Right Front Speaker Wire (+): Green
Right Front Speaker Wire (-): Orange
Rear Speakers Size: N/A
Rear Speakers Location: N/A
Left Rear Speaker Wire (+): Yellow
Left Rear Speaker Wire (-): Black
Right Rear Speaker Wire (+): Orange
Right Rear Speaker Wire (-): Blue


hope this helps out!

check for connection, might be the front right speaker was connected to right rear soround out, check recording if dolby pro logic or DTS system

Do you have the manual if not go here.
http://www.hammerwall.com/Manuals/Pioneer/Description/VSX-D608/Pioneer%20Home%20AV%20Receiver/L0020200/

Most music does not put out sound from the rear speakers. Test it with a DVD, most of them use the rear speakers for some sound effects.

Yes all speaker must be connected in order for them to work properly.  Also note that the audio that you are playing through it must be dolby digital 5.1 or higher or DTS.  If you are simply watching a tv program most of them will not be in surround sound as well as music discs.

1995 Ford Windstar Car Stereo Radio Wiring Diagram
Car Radio Constant 12v+ Wire: Green/Violet
Car Radio Switched 12v+ Wire: Yellow/Black
Car Radio Ground Wire: Black/Light Green
Car Radio Illumination Wire: Green
Car Stereo Dimmer Wire: N/A
Car Stereo Antenna Trigger: N/A
Car Stereo Amp Trigger Wire: N/A
Car Stereo Amplifier Location: N/A
Front Speakers Size: N/A
Front Speakers Location: N/A
Left Front Speaker Positive Wire (+): Orange/Light Green
Left Front Speaker Negative Wire (-): Light Blue/White
Right Front Speaker Positive Wire (+): White/Light Green
Right Front Speaker Negative Wire (-): Dark Green/Orange
Rear Speakers Size: N/A
Rear Speakers Location: N/A
Left Rear Speaker Positive Wire (+): Light Brown/White
Left Rear Speaker Negative Wire (-): Light Brown/Yellow
Right Rear Speaker Positive Wire (+): Light Brown/Green
Right Rear Speaker Negative Wire (-): Brown/Pink
-->

remove the front speakers cables from the rear-remove surround speaker cables from the rear and put them in the place of front speaker-run a music if you get good sound the problem in your front speakers(speaker or its cable)-if you got nothing you will have a problem in your system itself and need to fix in service center.

it is highly likely that you're TV is outputting mono sound, hence the left channel only. check your physical connections to the TV and the balance / channel volume on the television as well.