Failed upgrade f36 to f37. Please help!

There are several post here on the forums where we ( The community ) have successfully recovered systems from similar crashes. So if you want to I can begin to instruct you on this but you will need to have a Live USB ready to go.

Yes, but to be honest, your system has entirely mismatched packages. There is nothing to recover. If you have specific configs and files you need, back those up. The process we will do should not destroy your partitions and personal files, but it’s always good practice to back up your personal files.