Michael,
I have no experience with Verizon hosting, but if you don’t have a way to access your database, then you really don’t have what you need to effectively manage your site. Someone must have been able to access it in the beginning to install your current blog….maybe someone at Verizon did if for you, or maybe they just gave you an already installed blog…I’m just guessing here.
You said:
I downloaded everything from the server back to my PC from the website, which should include all of the data stored in the Blog (in theory).
I would not assume that unless you have looked in that backup and see your database. If you don’t have your database, then you have NONE of your data except for your uploaded files–images, documents, etc.
In short, if you have no way to access your database through phpMyAdmin (or something similar), then you really need to think of getting a new host if this is important to you.
Now, having said that, here is a suggestion…use at your own risk since it seems you have no way to backup and download your database first–which is what you should always do before attempting an upgrade.
— If you have downloaded your current source code from the server, then…
— Login to your server, create an empty directory, call it something like wpOLD and move all your current WP files into that directory, EXCEPT for your config.php file
— Upload the new 2.7 source code to the same location your old source code was located
— If you had any custom themes uploaded, then upload them from your backup (or from the wpOLD to your new install).
Then visit your site in your web browser…if all is well, you should be able to login and upgrade your database.
If this all works, then at least export your blog using the export feature in the admin so you will at least have that backup of the contents of your database.
Then, I would strongly recommend finding a new host where you have complete access to not only your files, but also your databases.