It would have been nice to have a Disk Image in advance.
At this point, I'm not sure I can offer any definitive advice as to how to proceed.
It doesn't sound to me like the computer, in its' current state is of any use and even if you managed to somehow create a disk image now (perhaps by booting from Rescue Media), I'm not sure that, that Disk Image would be of much value other than of course capturing and preserving you critical data which is very important.
Again..... as I said above, sooner or later you are gonna have to reboot the beast.
Might as well get it over with. Who knows, you might be surprised.
I wish I could say, go here and click this, do that and all will be well, but.....
As I understand it you are setting there with a computer that is for all intent and purpose, unusable.....
Unless I am misunderstanding your current situation.
If the computer is, in fact usable to some extent presently, then I would certainly seize the opportunity to copy off your user profile at least just to make sure that your documents, music, pictures, etc., were safe at least.