Hi Kate,
First thing that we should check is the Event Viewer (Quest Web Parts section) for any errors/warnings. e for the ULS.
If there is any error related to QWP installation try to fix it (ie: insufficient privileges, etc).
Then from teh Central Administration try to retract/redeploy QWP wsp package. Check again Event Viewer and ULS if that doesn't solve the issue.
Please let me know how it goes.