Provide warnings on download page if the private file directory is not writable

Here's my situation. I built a simple drupal site on a subdomain of my website. (http://testsite.example.com) I regularly used the Backup and Migrate module to download backups of the database to my desktop.

Recently we migrated the drupal site to another domain/server. It's been running well but now the D7 core and some modules need updating. (security updates needed of CKEditor and Webform Validation and general upgrades for Webform and Webform Conditional) I've backed up the whole site directory and want to backup the database as well. But Backup and Migrate no longer let's me do a (Quick Backup) download of the database to my desktop anymore....and backups are a prereq for doing updating to core and modules!

There is now a yellow flag warning at the top of the Quick Backup page. It says "You must specify a private system path in the file system settings to backup to the server" (I'm not sure why it's telling me this because I haven't chosen anywhere to backup to the server....I'm downloading...) In that warning is a link to 'file system settings' which takes me to Home>Administration>Configuration>Media page. At the top is a red x warning block warning of needed security updates plus these two bullets:

• Warning: mkdir() [function.mkdir]: Permission denied in drupal_mkdir() (line 2293 of /homepages/16/d207839233/htdocs/web/ephrataproject/includes/file.inc).
• The directory /hermes/web01/b2366/moo.andyvisualscom/Test-Sites/tempdir does not exist and could not be created.

Under that are the three fields to enter the Public File System Path, Private File System Path and the Temporary Directory. Here is what is in those fields.

1. Public File System Path = sites/default/files
2. Private File System Path = EMPTY
3. Temporary directory (with red outline...indicating problem here?) = /hermes/web01/b2366/moo.mysitecom/Test-Sites/tempdir (The "mysitecom" is the site/domain of the place where I first developed the site before the migration

I uninstalled the module - unchecking it in Administration>Modules and deleting it from the modules folder in Sites on the server. I thought that would take care of the moo.mysitecom/Test-Sites thing. Then I reinstalled the module and turned it on but got exactly the same thing. I also tried to set up another destination and send it to my email but still no-go with warnings...

Security update needed immediately red warning box is everywhere including on the Quick Backup page - and after hitting the Backup now button more points are added to it, such as:

1. The file cannot be written to.
2. Could not complete the backup.

I'm now stuck in this catch 22 - can't backup but need to in order to update things that are probably causing the Backup and Migrate to act funny... Also, did I mention that the server this site is now on is not one I own. An acquaintance has set up the database and directory ect. I only have FTP access to the site directory and can upload/download modules/css etc - but I do not have database or htaccess file access.

Any help with this would be greatly appreciated. Tips on how to give that help. I am not a developer...I do HTML/CSS and clicking buttons and filling in fields in Drupal... If you throw PHP etc at me - it probably won't help - unless you tell me in very detailed ordinary language where to go and what to type in - step by step. Just trying to be helpful and I hope it makes it easier to help me. Thanks.