The model of the TV I've got is kind of old, but is pretty big and I'd like to watch movies on it, played from the computer. I'm not a specialist, but does any of you guys have any experience with this situation?
You could use a HDMI to SCART converter like this one.
Operation is fairly simple, you take the HDMI output from your computer and plug it into the HDMI input on the converter, then plug your TV's SCART cable into the SCART output on the converter.
Since your computer has a VGA output, add a VGA to HDMI converter like this one.
VGA output -> VGA to HDMI converter -> SCART Converter -> TV input.
You will probably need to match the output resolution with the resolution of your TV.