I have looked at your code and found the following:
First things first. You need to move AWAY from using ToolParts and the SharePoint native webpart. they are deprecated and are a remnant from SPS2003. In MOSS / WSS 3.0 you can and should use the ASP.NET WebPart.
Secondly, I think you are mixing things up. The ToolPartGetLists is not a toolpart, it is a webpart, that in itself loads the CustomToolPart, which in turn allows you to select a list.
This toolpart is only shown when you edit the shared webpart in the UI. The list you select is then persisted to the SelectedList property of the webpart using the toolpart.
The connected webpart then tries to read the SelectedList property I guess.
Like I said, I could go and try to fix the code for you, but it is not the way to go, you really (REALLY) need to switch to ASP.NET WebPart based webparts. The native sharepoint one WILL be fased out in the (near) future.
Here you can find an example, with code! (scroll to bottom for download link). As a bonus, it uses the built in sharepoint listpicker