Execute the cells one at a time, starting at the top. When you encounter the first error, read the message and work to understand it. It could be that something is missing. For example, if the cell is trying to import something, it may be missing or the directory is wrong. If that's not the case, look up the documentation on the functions being executed. (Put the cursor in one and hit F1.) If the cell is complex, with many functions, break it apart as needed to diagnose the components. It is probable that the many errors all begin with a single cell that produces an unexpected output, which is then used downstream and generates a cascade of errors.
Generally, Mathematica has been good at backward compatibility. The problem is probably simpler than it appears. If the work is not proprietary, and not overly large, you could post the notebook by attachment and let the forum denizens have a look.
Kind regards,
David
