You need a new TV.
Anamorphic DVD's will play properly when you use component input. Their picture should be wide. There will still be some black top and bottom area particularly for the higher aspect ratios like 2.35:1. 4:3 and widescreen non-anamorphic DVD's will not play properly. Try S-video for them.
Keep the player on 16:9, not 4:3 letterbox.
Some DVD players do a "4:3 horizontal squeeze" that is different and separately selectable with or without the the player's "4:3 letterbox" mode, specifically to deal with TV's like yours.
Video hints:
http://members.aol.com/ajaynejr/video.htm