Have you taken a look at this thread: http://www.mojoportal.com/Forums/Thread.aspx?pageid=5&mid=34&ItemID=3&thread=2523&postid=11282 ?
Also, there is medium trust documentation here: http://www.mojoportal.com/mediumtrust.aspx. You must do more than set the RunningInMediumTrust key in the user.config for mojoPortal to work correctly in a medium trust environment.
Sub-domains aren't always setup as separate websites with GoDaddy, but rather as virtual directories with sub-domain names pointing to them. This is a very screwy setup but expected with GoDaddy so if you are using a sub-domain, make sure it is setup as an actual website.
Considering the log file doesn't have any errors in it, I would make sure the Data directory has write permissions assigned to the web user. The App_Data directory also needs write permissions assigned to it but that shouldn't affect the log.
If you still can't get any errors written to the log, try turning off Custom Errors by finding the following line in your web.config and changing the mode to Off.
<customErrors mode="RemoteOnly" defaultRedirect="Error.htm" />