How to salvage a paper when the lead author gave up publishing it and refuses to communicate

I suggest that you try to get the professor to arrange a three way meeting to resolve the issues. I'd also suggest that you be generous about who is a co-author and even who is first. Any forward movement is probably better for you than letting it go. There will always be other papers and you might be able to use this as a basis for future work if you can get it out the door somehow. But the prof has a bit of leverage, just from position. Moral authority if nothing else. The other shouldn't be in a position to hold you back, but need not participate in the future.

I think the professor owes you this much if she got you into the project in the first place.

If you wind up doing the rest of the work on your own, but others are co-author, you still need their permission to publish it, of course. Hopefully this won't be a block. But the professor may have a role here, as well.

Possibly not related to your case, but I have had somewhat similar experience before. One aspect you maybe haven't considered, and maybe more or less likely depending on the field, is if there was some underlying issue with the paper or results themselves.

I have had a case or two, most often when working with newer students, that a seemingly great paper and something that we can publish ended up having mistakes that were missed. It may be that some of the reviews, unless they were purely grammar issues of the paper, hit upon something the student didn't realize or had not considered important when first doing the work. For example, I recently had a student have some really interesting and unexpected results analyzing a dataset. They were writing the paper and explaining the results of why this would happen. It was a matter of happenstance that I had known the dataset very well, and eventually figured out they had duplicate data that should have been processed and removed. The student never realized this until I mentioned it. When we walked through each step together, they started finding more issues.

It may not be your collaborator losing face over the reviews, but possibly losing face over a mistake they made that they didn't originally notice.

Again, maybe this doesn't apply to your situation, but as an answer to the general question it may be something for others to consider, which is in generally a tricky situation and what requires trust with people you collaborate with.

So with that in mind, to actually use this as an answer, I would first go through the paper and any results that the first author did to make sure there are no problems with the paper. Then I would do a first draft to make any changes to the document and send to the student just asking 'do these look okay with you to submit?'.

On the other hand, I would take into account how much work you spent on the paper and how much effort it is taking to get a response. It is a little strange to me that you don't even have the manuscript. I am not clear by your post what your contribution on the paper is if the student did most of the work and writing, but you not having the manuscript sounds like they did all of the writing. With so many unknowns, it may not be worth salvaging.