Problem with Time Machine

Yikes! I don't have an answer for you, but a couple of suggestions. I have an Early 2008 24" iMac that has run Snow Leopard (and now Mountain Lion) well, so I do recommend the upgrade.

You could look for Time Machine messages in the system log file. TM reports general events and errors there. To do this, open Applications-->Utilities-->Console.app. Make sure the log list is showing in the left-hand pane (View-->Show Log List). At the top of that, under System Log Queries, select All Messages.

The newest messages will be at the bottom. TM messages come from com.apple.backupd, so look for that (or put that in the filter box at the top right). You can probably follow the beginning of the backup that way, and hopefully there will be a useful error message that will give you clues or at least more to google on...

The other idea is to use Carbon Copy Cloner or Super Duper to clone your internal HDD to your new external drive, thus doing the backup that way.

In any case, after a successful backup, I'd erase the internal drive and do a fresh "clean" install of Snow Leopard, and then use Migration Assistant to copy all the users and setup info from your backup (either the cloned disk or the TM backup should work for this, again, assuming the backup was successful).

Hope that helps. I use TM and love it but have never heard of your specific problem...

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Another thing occurs to me -- perhaps it is some kind of hardware error, judging by the grey screen. If you have your original discs that came with the iMac, you can boot from them and run the Apple Hardware Test. I think that's what I'd do first.

Well, I think you've found the right file -- I hadn't realized it but the system.log file is where my backupd messages go.

Look there again -- the backupd messages will only show up then the backup is run, so you need to look back to when you ran TM the last time. Use the filter with "backupd". Or, perhaps your system.log doesn't go back far enough. In that case, look in "system.log.0.bz2" (that's a zero), "system.log.1.bz2", etc. to go back further in time. The backupd messages have got to be somewhere in there, I'm sure!

Not sure about the fatal exception for the ATS framework as I don't know offhand what that framework is for, but I'd guess it's not the cause of your TM problem.

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EDIT: the older system log files I talk about are under "/var/log" in the log files pane.