Try a couple of resets first, if you haven't already.
Here's the [link|https://www.sony.com/electronics/support/res/manuals/4178/41788271M.pdf|Operating Instructions|new_window=true]
Here's a link to the [link|https://www.sony.com/electronics/support/televisions-projectors-lcd-tvs/kdl-32ex700/articles/00200862?cpint=spt-banner_00248776_tv_ts_guide_i|troubleshooting guide|new_window=true]
Procedure for a Power Reset: (I would suggest that holding down the power button for a minute be added between the first and second steps)
# Unplug the TV power cord from the wall outlet.
# Disconnect all devices from the TV.
# Wait five minutes and then plug the power cord back to the wall outlet.
# Connect the first device to the TV.
# Turn on the TV again.
# If the problem still occurs, repeat the above procedure for each of the devices that you have connected to your TV. If it turns out that one of the connected devices is causing this issue, contact its manufacturer for support.
There may be a factory reset procedure you can try, but that erases any stored data you have.
[link|https://www.manualslib.com/download/1581328/Sony-Kdl-32ex700.html|Here's a link to the service manual|new_window=true]
If resets don't help, a first guess is the TCON board, which is a small board in the lower center of the rear of the TV when the rear cover is removed. You did not mention blinking lights on the TV which would be significant, as these models use a blink code on their standby light for troubleshooting.
Second guess is the LCD screen itself. Section 3 of the Service Manual seems to indicate that in the triage section.