Hi
I'd suggest you to export the lists as list templates (including the data) and use them in a different site to recreate the lists. Then use a qChartView to display the data.
While you're rendering the data please open SharePoint's ULS log file to see if you get any error/warning related to this process.
Also I assume that the fields you use in the qChartView are common to all lists you try to aggregate in the qChartView.
What's the QuickApps (Quest Web Parts) version?
Please let me know how it goes.