Web-part issue after migrating from 2010 to 2013

Question

Hello all
Correct me if I am posting this question in the wrong section.
The background is: Migrating and Upgrading SP2010 to SP2013. I did it, and alot of it works, as it should, though I have one issue.
I did deploy all the solutions to both the 14 and 15 hive, and activated all the propper features. Now, I have one web-part which breaks down. It is a Web-part that communicate with a SAP endpoint, to retrive some data and show dem. The Web-part work fine in
the 2010 environment.
As soon as I enter the site where the Web-part is placed in, I am being redirected to the "Maintanence Web-part, error message". If I delete the Web-part I can access the site with no errors. The code works fine in 2010. 
The error I am getting is "value cannot be null".
Unexpected System.ArgumentNullException: Value cannot be null. Parameter name: uriString at System.Uri..ctor(String uriString) at Microsoft.SharePoint.SPSite..ctor(String requestUrl) at MyWebPart.Core.ListConfiguration.<>c__DisplayClass1.<GetKeyValue>b__0()
at Microsoft.SharePoint.SPSecurity.<>c__DisplayClass5.<RunWithElevatedPrivileges>b__3() at Microsoft.SharePoint.Utilities.SecurityContext.RunAsProcess(CodeToRunElevated secureCode) at Microsoft.SharePoint.SPSecurity.RunWithElevatedPrivileges(WaitCallback
secureCode, Object param) at Microsoft.SharePoint.SPSecurity.RunWithElevatedPrivileges(CodeToRunElevated secureCode) at MyWebPart.Core.ListConfiguration.GetKeyValue(String key) at MyWebPart.OrderCatalog.OrderCatalogUserControl.FillFilterBoxes() ... 438bb29c-c202-3049-9aab-e895c85176d5
Unexpected ...at MyWebPart.OrderCatalog.OrderCatalogControl.Page_Load(Object sender, EventArgs e) at System.Web.UI.Control.LoadRecursive() at System.Web.UI.Control.AddedControl(Control control, Int32 index) at MyWebPart.OrderCatalog.OrderCatalog.CreateChildControls()
at System.Web.UI.Control.EnsureChildControls() at System.Web.UI.Control.PreRenderRecursiveInternal() at System.Web.UI.Control.PreRenderRecursiveInternal() at System.Web.UI.Control.PreRenderRecursiveInternal() at System.Web.UI.Control.PreRenderRecursiveInternal()
at System.Web.UI.Control.PreRenderRecursiveInternal() at System.Web.UI.Control.PreRenderRecursiveInternal() at System.Web.UI.Control.PreRenderRecursiveInternal() at System.Web.UI.Page.ProcessRequestMain(Boolean includeStagesB... 438bb29c-c202-3049-9aab-e895c85176d5
Unexpected ...eforeAsyncPoint, Boolean includeStagesAfterAsyncPoint) 438bb29c-c202-3049-9aab-e895c85176d5

Answer 1

No, I did not migrate the content from 2010 web-config to the 2013 server. This is something I will take a look at, to see if there are some missing points in the config-file of 2013.
And just to be sure, when we are talking about the config file, it is the one who is associated with the Web-applikation? So, IIS --> WebApp --> Explorer --> and that web.config?