Sounds like an installation and configuration issue.
First I would check into SharePoint Central Admin page -> Solution Management and verify if "Quest Shared Web Parts.wsp" solution package has been properly added/deployed. I would try to retract it and redeploy it to see if any error occurs.
Second I would go check GAC and look for WA.Common, WA.Core, WA.Resources and WA.Web Parts assembly DLL presented in GAC.
Third I would check the SharePoint web application configuration file and make sure the SafeControl entry is added properly:
<SafeControl Namespace="WA.WebPart" Assembly="WA.WebPart, Version=220.127.116.11, Culture=neutral, PublicKeyToken=2b4b09f1c57c8f0b" TypeName="*" Safe="True" />
Lastly, if you have installed previous version, you need to go to Control Panel to uninstall it first before running the new installer and make sure the uninstallation completely removes all files include the solution package.