New Install with an old database?

Something got screwed up with my site and I don’t know what. It just gets an error message on the first page. The hosting company has no idea what went wrong, as it has worked for month and months with no issues. I didn’t recently update anything so I know it wasn’t that. It started out with a “fatal error in file version.php” and has since changed to “Parse error: syntax error, unexpected ‘(‘, expecting ‘)’ in /wp-includes/plugin.php on line 79”.

Either way, it was time for a site update so…

Can I remove all the files from the server, and then upload a fresh install of WP and just use the old database information?

The url is staying the same and the site name and stuff is staying the same.

Can I do this? How?