If you have your old database and uploads folder, you can install WordPress and give it that database.
Then, you can use the wordpress importer/exporter to export the posts, then upload it to your new site using the same plugin.
If your old site is much larger, it may even be easier to take an export of your new site, then upload the old sites database and import the new posts into the old site.
This should handle the post content and all the tags