This article answers common questions about getting an old TV to work:
https://antiqueradio.org/howfixtv.htm
As Electronic M noted, recapping (replacing old paper & electrolytic capacitors) is pretty standard, for safety and reliability reasons.
I restored a very similar Zenith TV twenty years ago. It, too, made a picture without any restoration:
After restoration, it looked better and I'm more confident about playing it:
An advantage of restoring a set that already "mostly works" is that you can turn on the set and play it briefly, after replacing every couple of capacitors, to make sure you haven't made any wiring mistakes. If all goes well, you'll see things gradually improve, as you replace more and more bad old caps.
Regards,
Phil Nelson
Phil's Old Radios
https://antiqueradio.org/index.html