Looks like you already disabled votes count in the listing page (from options ofcourse).
In order to disable voting on old polls, you need to set voting expiry date on your poll. For example you can set the date while creating the poll and the poll will be opened only till that date. After the Voting End Date, users can only see results if you enable viewing results permission.
corejoomla.com is not affiliated with or endorsed by the Joomla! Project or Open Source Matters. The Joomla! name and logo is used under a limited license granted by Open Source Matters the trademark holder in the United States and other countries.