@fneto4 About using a CRT TV via composite cable, I just answered another post with a similar situation, please check:
https://forum.recalbox.com/topic/25248/can-not-use-the-composite-output-in-recalbox-7-2-2-on-my-raspberry-pi-4b
HDMI
Have you tested your Rpi on another TV without an adapter?
Can you test with another adapter?
Are you testing with the correct HDMI port on the RPi4?
Have you tested with another HDMI cable? There are several versions of HDMI cable, not to mention the quality of the cable...
Have you checked if it's not some setting on the TV?
HDMI converter to VGA
Signal converters usually don't bring the expected result, they don't always manage to make the ideal communication between the RPi and the TV (since they make a conversion).
A signal converter is literally like an automatic translator: sometimes the translation is so mechanical that you can't understand it even after the information is in your native language.
In short, the converter needs to correctly identify your TV's EDID, and convert that to RPi. When the converter can't even recognize the edid, the whole conversion goes bad, so one possibility you have is to force an edid configuration manually, as per the options mentioned in the official raspberry documentation:
https://www.raspberrypi.com/documentation/computers/config_txt.html#hdmi_ignore_edid
There are some users who claim that a DVI adapter works better, but I've never used it either, and there are many different makes and models, so I can't say:
https://forum.recalbox.com/topic/24295/message-hors-de-portée-écran/2
Generally speaking, video adapters are not a good idea, use them only if they are the last option. And unfortunately, we don't have a lot of user reports showing which makes and models are working, and without those user comments, we don't know either.