Restoring from files?

I manage(d) an externally hosted WP blog. It became infected and the entire contents of the server were wiped. I have a pre-infection copy of everything on the server, but never used the export tool or performed any explicit backup operation. Everything I’ve turned up my research indicates that my blog is lost. Obviously, I hope this is not the case. But, if it is, I would at least like to understand what it is that I am missing. Could someone explain this to me or point me to a good resource?

I understand that posts are not files but objects in an SQL database, a language of which I am totally ignorant. But where is this database if not in the collection of files in the directory containing the blog? Even if it is not possible to simply upload the files to the appropriate directory (tried this, of course), shouldn’t there be some other way–even if it would require hiring someone knowledgable in SQL?

For instance, I did a clean WP install in the directory that had housed the blog before it was wiped and then selectively copied material from my backup over the install (same version 4.1), but this did not work at all. Is this the sort of thing that someone knowledgable about the SQL and the WP file structure would be able to do? Maybe being more carefully selective about what to overwrite and manually editing some of the PHP files?

Or are there any other options I might consider?

Many thanks for any advice you are able to offer.

Patrick