Upgrade froze at 4.7.8, Can't find valid value for qrid
The error message comes from refreshing the browser rather than the upgrade process.
The last entry before the error is:

Dec 21 12:20:56  [info] Running task: Upgrade mailing foreign key constraints


You can find the detail in CRM/Upgrade/Incremental/php/FourSeven.php
Adding foreign key constraints creates an index which can take a while on a big table.  How many rows (count(*)) do your civicrm_mailing_event_queue and civicrm_mailing_recipients tables have?

Once the upgrade has started, I don't know how dependent it is on the browser, so it would be worth checking the log later to see if you have any further messages from the upgrade.

If you need to start again, then I'd try this:


Restore your database and files back to your starting point at 4.3.8 (you did take full backups didn't you??)
Upgrade to 4.7.7
Check all is working as expected
Take new backups
Try upgrading to 4.7.8


If your mailing tables are large you'll need to be patient. If it fails, you can easily go back to 4.7.7 and then work out what to do next.