Adrian, I do not have any Windows Phone 7.8 devices (I got rid of all of them because of age) and kept a few WP8 devices as well as my WP10 device so I am not sure if the marketplace is not working. That said, this might be of some help.
Go to: https://support.microsoft.com/en-us/help/11696/windows-phone-7
Click on Download games and apps FAQ
See if that helps....
I have a feeling it might not because age is a huge factor and support has to come to an end at some point. It is worth trying IMHO