No database? Then it’s no use to you. Because it contains all the texts that make up the website.

Then I would recommend the following approach:
Make sure the hosting meets the requirements for 3.8.24. This might be the hardest part. I suspect PHP 5.6 and MySQL 5.0 should work.
In this hosting you download the ZIP from the release of 3.8.24, which can be downloaded here: https://wordpress.org/download/releases/#branch-38
You unpack this ZIP locally and upload everything unpacked to the hosting.
Then upload the wp-content folder and the wp-config.php from your backup.
Then you access the page via browser – does it work? If so, then you have restored it. If not, activate debug mode in wp-config.php as described here: https://developer.wordpress.org/advanced-administration/debug/debug-wordpress/ – this should allow you to analyze errors that occur in more detail.

If there are errors related to a plugin, remove it from the plugin directory. The same applies to the theme.

Alternatively, you could use a newer WordPress version instead of 3.8.24. But only in the way described above by downloading the official release. The first time you use the database, WordPress would have to recognize that it is older and upgrade it. I would recommend using a version of the 4 series for this so that the jump is not too big.

Only when you have achieved a stable WordPress should you think about upgrading to the latest version. Make a backup of the working system beforehand. Then you check whether there are updates for all plugins – if not, you would have to deactivate them. Same with the theme.