Hello, I'm TV Tech1 and I'll be working with you to identify and help you resolve your problem.
Yes, you are correct. the capacitors get leaky and require replacement to get the picture and sound back.
This guy has some good visual details on his video, but the Plastic issue is not as important as he shows. Plus it can confuse you.
The KEY....the silkscreened /Painted part on the board is the same as the Painted top of the caps. Me, I like to take a permanent marker and mark the board where the painted cap mark is pointed to.
I heat the one side of the cap to melt the solder, and just lift the cap with a thin flatblade screwdriver a little, then go to the other side, lift it a little, go back to the other side, lift a little more, back and forth until one side separates, then the other lifts off.
This second one is a little better...in fact I like his suggestion to use Blue Tack to hold the cap in place, and he does show how to "wrench" the caps off the board....I'm not keen on doing it that way....but it works for both of these guys.
Of course my soldering iron is a Weller with a sharp tip that can heat the pad to lift it off. Their equipment is a little bigger -- their "wrench off" procedure works for them.