Cannot run update.php, blank screen when I try that; Error messages

Drupal Newbie. I tried to Update, from Drupal Core 7.12 to 7.14. This is the first time I have tried to update Drupal Core and it did not go well.

The upgrade.txt file says to do the following, which I did:

6. Run update.php by visiting http://www.example.com/update.php (replace
www.example.com with your domain name). This will update the core database
tables.

If you are unable to access update.php do the following:

- Open settings.php with a text editor.

- Find the line that says:
$update_free_access = FALSE;

- Change it into:
$update_free_access = TRUE;

- Once the upgrade is done, $update_free_access must be reverted to FALSE

When I tried to run update.php I got a blank screen.

When I went into the Drupal Administration Panel, which was working perfectly before this stage of the update, I got error messages.

I get the following error if I try to browse the web site now:

Warning: require_once(/home/computer/public_html/drupal/includes/bootstrap.inc) [function.require-once]: failed to open stream: No such file or directory in /home/computer/public_html/drupal/index.php on line 19

Fatal error: require_once() [function.require]: Failed opening required '/home/computer/public_html/drupal/includes/bootstrap.inc' (include_path='.:/usr/lib/php:/usr/local/lib/php') in /home/computer/public_html/drupal/index.php on line 19

This is a test installation of Drupal, my first, on a cPanel Shared server. It had been working, perfectly, until now. Is there a way to salvage this installation, or, should I nuke it and start over?

Thank you, in advance, for your time and your help!