what is in the zip file? If it has a database dump, you might not need to restore ALL of the files…you might be able to simply restore your uploads folder, and your database, which is not too difficult.
The database dump will most likely be a single file ending with .sql
Can you post if you have that? If so, can you also say how large of a file it is (mb)
Also, meanwhile…if in that zip file there is a folder under /wp-content/uploads you can have a look in that folder, and then make a quick comparison of the files on your server under the same folder. They are date-named so you should easily be able to make out if you are missing folders/files
this will give you a better idea if it was just your database, or your entire wordpress installation that was down-graded