Hello, I'm TV Tech1 and I'll be working with you to identify and help you resolve your problem.
Windows startup screen's resolution is totally different than the final desktop screen's resolution and refresh rate.
Since you have the startup screen, you now know that the laptop, Hdmi to VGA converter and the TV set are fully operational "hardware-wise"
In other words, you don't have issues with the computer or the converter or the TV set having "broken HDMI parts"
And what it also tells us is that the signal coming OUT of the laptop doesn't match the list of "usable" resolutions/refresh rates that is coming out of the laptop/converter pair.
Now...startup screens are kind of the basic resolutions that all computer monitors have always used for years and years. They have to be generic, and in most cases either 640x480 or 800x600 at 60Hz refresh rate are used.
Your TV can read those. But what is your FINAL resolution you are set at when you look at your display's settings???
And....does your laptop also display on its screen while you are attempting to see it on the TV screen? Do you see BOTH when the startup screen appears on the TV set??
Also, on your laptop, if you right-click the desktop you should be able to access your FINAL resolution settings.
See picture, let's make sure the TV is getting a resolution it can work with, and you can always check the operation by setting it to 480x640 (too large) or 800x600 (better fit on TVs)
See picture --
Always start with what works....and your startup screen does show up on the TV set.
Keep that in mind, now set your monitor #2 to the startup resolution, check it, then walk the resolution UP using the TV's list of usable resolutions and see how the TV handles them.