First of all to troubleshoot your problem check what's happening behind the scenes.
1. Run Qlik Sense Desktop (and forget about it )
2. Go to G Chrome (preferable) browser: https://localhost:4848 (do not open more than 5 Qlik Sense tabs)
3. You will see your desktop HUB
4. Open App on new tab -> go to Load Editor -> F12 (open developer tools) -> refresh the page and check console for errors as well as Network section to see what is pending during loading connection list.
Share results, there will be more details for community to help.
Hm.. Connector is not responding... Is it registered or running at all?
Check <User>\Documents\Qlik\Sense\Log\ConnectorRegistryProxy\ logs... Is there any Errors there?
Another thing, are you using your own ODBC driver or Qlik odbc package?
If own ODBC, could you check if it works in other applications (Excel, QLikView , whatever)
If Qlik ODBC package, check logs (above), and try other connector for testing purposes.
Try to switch between native Qlik ODBC package and own ODBC (System DSN).
Connector is not responding is more connector issue than QlikSense OR QlikSense is looking for connector in a wrong place....
Hope this helps to trouble shoot your issue.