Thank you, I spent all day yesterday trying to resolve this issue with Hostgator. They just kept insisting that the error was in the coding and because of that there is nothing they can do.
I even copied a basic session script from this page https://www.php.net/manual/en/function.session-start.php, (https://www.parkingascars.com/page1.php) which didn't work and they still insisted the error was with that coding as well - unbelievable.
I have received an email today from support - again saying that the error is in the code and there is nothing they can do, yet I have just tried to log in again and it is all working, and the script on this page now works (https://www.parkingascars.com/page1.php. Maybe they didn't want to admit it was their fault - or something they did in testing fixed it without them knowing - but at least it is all working now. I have to say I wish I hadn't moved to Hostgator and wouldn't recommend them.