I can't think of a reason it would not work in medium trust, though for any serious ecommerce I would use a dedicated server not shared hosting and on a dedicated server you can use full trust.
I assume the problem is because you've deployed some funky build you made yourself.
When producing a build from svn you should not then copy in dlls from another download, you should compile it for the db you are using by setting correct project references in Visual Studio, then you can test and debug it against the database of your choice in Visual Studio.
You can test medium trust on your own machine using Visual Studio by uncommenting this in Web.config system.web section.
<trust level="Medium" originUrl="" />
You cannot produce a good package using the Visual Studio publish feature if thats what you've done. I use UnleashIt.
Hope it helps,
Joe