Not able to upgrade to latest version (2.16)

Earlier this week, I successfully installed Piwik on my website using the version that was provided by my hosting service. I ran it for a few days just to see what it looked like (very good!) and today I tried to upgrade to version 2.16 by clicking the button at top right. This told me that the database needed to be upgraded. I clicked the button to upgrade the database but got a blank screen. Returning to the update page, I copied the SQL statements and executed them manually using phpMyAdmin. I checked the database structure afterwards and all seems to be OK. However, when I try to access Piwik in the usual way, I just get the update screen again. What to do, please?

Try to download Piwik and replace the codebase (except the config file). Get Piwik - Analytics Platform - Matomo
Something must have gone wrong with the update process.

Thanks for replying. Unfortunately, what you suggest is not really practical due to the fact that my communication to my web host is via satellite. Uploading the entire code base takes hours due to the large number of files. Having done it once, I’m not inclined to try it again. I really need something which is more precise. The module which is generating the error message must be testing something and it would be helpful to know what it is. In the meantime, I’ve gone back to the old version.