Note: I use GoDaddy for my domains but my hosting for the domains is with discountasp.net
From what I've been able to discover you will not be able to climb above Medium trust on your GoDaddy account.
http://help.godaddy.com/article/1039
Recently Updated: March 5, 2008 4:44 PM
Trust level refers to permissions set in the Web.config file that dictate what operations can and cannot be performed by Web applications. Our ASP.NET 3.5 shared hosting servers use the default Medium trust level with the addition of OleDbPermission, OdbcPermission, and a less-restrictive WebPermission.
Applications operating under a Medium trust level have no registry access, no access to the Windows event log, and cannot use ReflectionPermission (but can use Reflection). Such applications can communicate only with a defined range of network addresses and file system access is limited to the application's virtual directory hierarchy.
Using a Medium trust level prevents applications from accessing shared system resources and eliminates the potential for application interference. Adding OleDbPermission and OdbcPermission allows applications to use those data providers to access databases. WebPermission is modified to allow outbound http and https traffic.
Fortunately GoDaddy provides you with girls to overcome the frustration: http://www.godaddygirls.info
Also recommend you take a look at Rick Strahl's article:
Running ASP.NET in Medium Trust
http://west-wind.com/weblog/posts/6344.aspx
Salute,
Mark