It would be an odd and unlucky coincidence that the HDMI ports on both 7950's are dead.
Have you tried booting into safe-mode with the monitor hooked up to the 7950?
Do you have another HDMI cable that you can use? Unlikely to be the cause, since the 5870 works, but it is worth a shot.
Before you re-install Windows I would do a manual driver uninstall following the guide in tsm106's AMD How To Thread
I have also used the DDU uninstaller, and it has worked well on my systems that have AMD chipsets. You can get the DDU uninstaller from Guru3D's DDU Thread
Before uninstalling the drivers, if possible, you should do a system restore to a time before you used CCleaner or regedit. This will ensure that the registry didn't get nuked when you originally uninstalled the drivers. After doing a system restore I would uninstall the drivers, following tsm106's guide and then use DDU in safe mode.
After the drivers are uninstalled, I would power down the system and then install a single 7950 in the primary slot and see if you have video from the HDMI port.
Good luck getting this sorted out.