Timor, sorry I work during the day.
Your video shows conflicting information. Remote connected(solid Green) Drone disconnected (quick yellow flash) this is not unheard of for the P3S.
The P3S is known for it's being Twitchy.
First, Take the Props off of it! Your not trying to fly it, you are trying to get it to work.
Second, You absolutely have to follow start up procedures to the letter of the law.
Turn everything off. Make absolutely sure that the remote and the drone battery are FULLY charged.
Turn them on in this exact order. Remote first, Then phone, THEN Drone.
3rd Try the link procedure again. But watch the Link light on the drone! Ignore the phone. You can worry about that later.
Until the drone and the remote controller agree, all else is mute. Don't assume anything. If it doesn't work, start over.
Once you get this accomplished, you shouldn't need to do it again.
If you have the manuals, Read them from Front to back. If not, Go to DJI Phantom Accessories & Tips | Phantom Help. You will find absolutely everything you didn't want to know about DJI Drones plus a lot more. Failing all else, go to phantomhelp.com, pull down the phantom 3 standard, go down to reference, Phantom3 and select the Summary PDF.
DJI help and support is useless. The Phantom series must have been one of DJI's first shot at writing software. And I don't think they ever got it right!
The phantomhelp page should become one of your friends. That and PhantomPilots forum.
I REALLY appreciate your support on this- it's driving me mad! I do keep trying the procedures, -without props, and again, when the r/c and drone were in close proximity - on the table at home, the lights seemed to sync. Then I take it outside and it goes back to the old amber flashing, despite me going through the very useful procedures you and Oso have referred to earlier.
I'm going to start again and follow your recommendations EXACTLY...
Thanks
T