I've got new information. I installed the ATI Catalyst Control Center via Ubuntu's "Restricted drivers available" GUI and suspend WORKED! It even resumed quickly, turned on the backlight, and gave me a login prompt.
If you ever suspend, even once, it seems that the MBR is corrupted. After suspending and resuming once, if i then choose "Shutdown" (or sudo poweroff) the system will refuse to turn itself off entirely. I then hold the power button down for 5 seconds to turn it off. When I turn it back on, I get a blinking _ cursor for about a minute then "Reboot and Select proper Boot device or Insert Boot Media in selected Boot device and press a key." I think that this message is from the Windows 7 install on my drive.
I think this means that the MBR has been overwritten. To fix it, I have to reinstall grub2 as described here:
The salient command is:
(boot from liveCD)
Where 0d104aff... is specific to your system.
sudo grub-install --boot-directory=/media/0d104aff-ec8c-44c8-b811-92b993823444/boot /dev/sda
So, suspend works, but either it jacks up grub2 or the hard-poweroff does. Hibernate does NOT work when the BIOS CPU Information "E6" mode is disabled, but does when that's enabled.
I'd like to try setting up an EFI boot partition as described here:
Then, perhaps my suspend and hibernate can both work while using the ATI drivers.