Hello
Welcome to Apple Support Communities!
If we understand your post correctly, Migration Assistant keeps hanging and Time Machine isn't working either. We're happy to help!
How to move your content to a new Mac advises that it may take several hours to finish transferring the data.
If you quit the migration before it has a chance to complete, you can restart it again to see if you can get the rest of the information to your new Mac.
Also, have a look at this article, Back up your Mac with Time Machine, for the issue with Time Machine.
Let us know if you have any questions.
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Take care!