JQuery Conflicts

I have taken over the handling of a website from another web developer who used jquery to perform some tasks on the site. I still need these tasks to function, but they are conflicting with a plugin I am trying to use.

The plugin is trying to use the built in WordPress jquery library.

This is from my header that is calling the conflicting library:

<script src="https://www.google.com/jsapi?key=API key:
AIzaSyAHl6Eu42bAkQoy8twZkf5IC6ShzMFoDOo" type="text/javascript"></script>
    <script src="https://maps.google.com/maps/api/js?sensor=false&key=AIzaSyAHl6Eu42bAkQoy8twZkf5IC6ShzMFoDOo" type="text/javascript"></script>
    <script src="https://ajax.googleapis.com/ajax/libs/jquery/1.4.4/jquery.min.js"></script>
  	<script src="https://ajax.googleapis.com/ajax/libs/jqueryui/1.8.9/jquery-ui.min.js"></script>

  	<script src="/wp-content/themes/sullivan/library/scripts/jquery.cycle/jquery.cycle.all.min.js"></script>
  	<script src="/wp-content/themes/sullivan/library/scripts/pngFix/jquery.pngFix.pack.js"></script>
  	<script src="/wp-content/themes/sullivan/library/scripts/lazyload.min.js"></script>
  	<script src="/wp-content/themes/sullivan/library/scripts/core.js"></script>
  	<script src="/wp-content/themes/sullivan/library/scripts/jCsetup.js"></script>
  	<script src="/wp-content/themes/sullivan/library/scripts/slideshow.js"></script>
  	<script src="/wp-content/themes/sullivan/library/scripts/jquery.jcarousel.min.js"></script>

The site is https://www.bsullivan.com