I just plugged a Dell 1704FPT via a DVI->VGA adapter into my HD4850, (main monitor is a ViewSonic via DVI), and rebooted.
Both monitors displayed BIOS info, the ViewSonic displayed Windows 7 startup, and then when the Desktop came up on the ViewSonic it was extended to the Dell.
Using Catalyst 10.12 here on 7HP x64 but not SP1.
You haven't said whether the Sony will function if it's the only monitor plugged in.
Have you checked the Sony website for monitor drivers?
Windows might not have correct/up-to-date drivers with the right frequency characteristics for the monitor.
According to Sony, Windows 7 is not on the list of supported OS': SDM-HX93