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Well, the end of the log file is pretty self explanatory:

ERROR |120821 14:58:38|Akeeba Engine has timed out

ERROR |120821 14:58:38|Akeeba Backup has timed out. Please read the documentation.

In this case the documentation is here and asks you to try running the Configuration Wizard. So, the first step is to try clicking on Configuration Wizard, let it finish and retry taking a backup. If that fails please ZIP and attach the new log file.

Taking a look at your log file I see that the process halts when trying to backup the gtranslate/cache folder. What happens is that you're running your site on a Windows testing server and Windows is notoriously slow listing the contents of directories with hundreds of files (it needs several dozens of seconds). This causes a timeout in PHP which can't be worked around. The timeout happens inside PHP, when waiting for Windows to list the contents of the directory. I can't create a workaround to make Windows' file system management not suck so much or transform your slow hard drive into a blazing fast SSD. We can, however, do something to get your site backed up.

Judging by its name, this is a cache directory which means that the files in there should be skipped from the backup. You can use the Files and Directories Exclusion feature to exclude that directory.

If that is not desirable (even though I don't see why you'd want to back up unnecessary cache files) you will have to edit your php.ini file and set max_execution_time=600 and memory_limit=256M, save the file and restart your server environment. This allows PHP to wait the dead slow Windows file system code for up to 10 minutes to provide a list of the hundreds upon hundreds of files in that folder and give plenty of RAM to hold that list. Please note that I do not recommend this approach.

I see this:

INFO |120822 15:54:42|Scanning directories of <root>/gtranslate/cache

I wrote this as the recommended solution:

Judging by its name, this is a cache directory which means that the files in there should be skipped from the backup. You can use the Files and Directories Exclusion feature to exclude that directory.

The log file tells me that you didn't do that.

You only changed the PHP settings. Remember what I wrote about it?

Please note that I do not recommend this approach.

And I wrote that because I know that Windows sucks at filesystem I/O and would probably fail to list a folder with thousands of files in a timely manner.

So we go back to my previously suggested solution. You can use the Files and Directories Exclusion feature to exclude the gtranslate/cache directory.

Please note that the directory in question is a cache directory. By definition, caches contain redundant copies of information available elsewhere, with the only purpose of rapid access. Cache information is supposed to be transient and expendable. Backing it up is a waste of resources and, in your case, a source of unnecessary grief. Just skip the contents of that directory, you don't need them. As soon as your site is accessed in a different language, GTranslate will fill up its cache.