Alright, today I have also tried the HD7750 and the HD7770 on a MS-7358 V1.1 Motherboard with Intel Bearlake G33+ICH9R chipset (published in 2007) with PCI/E 1.1 slot in a Medion computer. After upgrading the BIOS to V1.1D (dating from 2009, available on the Medion homepage) it worked ! I have found similar information elsewhere that confirms the experience.
On the other hand I was sadly unable to find such an update for the VIA P4M900 or Intel 945GL chipsets which were published in 2006, so I am afraid those lovely mainboards have seen the best of their days ... but don't worry, replacement is easy as compatible motherboards are still offered for around 70 Euro that will allow you to keep everything else besides the motherboard ;-)