I understand you are experiencing issues trying to set proper screen resolution for your LCD TV model LCT3285TA.
According to the specifications of the TV, the native resolution is 1366 x 768. At this point, it looks like the TV EDID is not been detected properly. You need to make sure that you install the latest TV firmware or monitor drivers. Also, check cables, and be sure they have same end on both sides of the cable.
Here is the link for the latest video drivers:
Please filter by operating system and try to install the driver when it finishes downloading, to verify that your system will accept it.