The red light just indicates that there is some kind of error and the phone can't boot. The video you linked to shows the repair (a very cool one by the way) of just one possible error, but it could as well be software related. Check out this post, maybe reseting the phone works for you: No Power & Not Charging
Just as an additional info: I got myself a Sony Xperia Z1 Compact and changed the battery after the first one was dead. Because of the broken sealing some water managed to get in later and I also got the red light as an error. I opened the phone again and dried it out, also had to exchange the display, but it works again for now.