You will have a hard time finding a slideshow that does not run jQuery . You may want to try another slideshow module though. One that encapsulate jQuery code differently. It will be a good way to check if the problem was coming from the old one.

Hello,
that my be another problem all together. Anything that can stop a slideshow from working. One little script conflict and the whole thing can break.
If you can, post a URL where the issue can be seen and there may be something obvious in the source code.

3 jQuery libraries are loaded in your page and they are NOT compatible with each other (jQuery 1.6, 1.8 and 2.0).
For more information on the differences, please go to jQuery.com.
Very few scripts are ready for jQuery 2.0 so you should try and avoid using it. There is an error when your script loads actually, you are missing the subversion number.
Does the module swmenufree has an option to disable jQuery? Do you know what extension loads jQuery 2.0?
If you cannot get rid of those issues, try enabling the jQuery Easy plugin and set the version to 'Joomla' if your version of Joomla! is 3+. Otherwise, set jQuery to version 1.8.