Hi,
Sorry for the issues you are having.
I can help out.
Do you have any custom templates in your theme for the widget?
With 3.10 we had to make some changes and if you do not update those custom templates the Events will not show.
In the list-widget.php template you can add these to the top and that might fix the issue instead having to redo custom work:
$events_label_plural = tribe_get_event_label_plural();
$posts = tribe_get_list_widget_events();
Let me know how that works out.
Cheers