LCD handheld TV not displaying colour
 

I bought a 1985 Citizen TC53 earlier this
year and used it with a VCR several times.
Yesterday, it was displaying in black and
white and the batteries had leaked. I
replaced them, cleaned the compartment
and tried adjusting brightness and colour.
Nothing looks broken inside. I have a
multimeter but don't know what to test.

Corrosion and leakage due to electrolyte is possible. Is worth to wash the board and look for any strange spot in the tracks/parts. The contamination perhaps hit near the chroma circuits/crystal.

X2 on what Alex KL-1 said. If you haven't opened it up yet, I'd do it now and wash any battery juice with vinegar and then rinse with water.

Also there there are quite a few surface mount electrolytic capacitors that are failing in these little TV's. One of those could be getting weak causing the no color issue.