My macbook is stuck on grey screen

I cannot get to my desktop. This started 2 days ago, leaving it off doesn't help. Battery is fully charged but does get very hot very quickly - this is new in the last 2-3 weeks.

I do see other questions here but they aren't addressing my concern. I just need to get to my desktop and use iCloud to transfer to my new macbook - or to at least restore from my external hard drive.

There is no way to get out of this grey screen either, other than using "power on / off" and I'm concerned that using this shut down method all the time may do further damage. The overheating that is suddenly occurring is a concern as well. I'm not certain of my OS without being on there to check but the one I've listed is close.

Any help much appreciated.