If you tried 2 different PS3's then a dedicated Blu-Ray player won't solve your problem. Its not the cable as it will either work or not work. Make sure to try 2 different disc's to eliminate a bad Blu-Ray. I don't know what LG's 3D world is but if its an app it is most likely in t/b or Side by side format. It still points to the TV maybe a setting , a defect with the HDMI input or 3D processor. I would try a factory reset on the TV or maybe a firmware upgrade.
Smart enough to know better, to old to care