I added my own "modx’d" version of slick slideshow (similar idea to easyslider) and I was having issues with ajax search conflicting with jquery as well. I just wanted to say thank you. All I did was a find "$" and replace all with "jQuery" (minus quotes of course) in my slideshow javascript and it began working. Apparently jQuery uses the $ as a variable for "jQuery" to reduce the size (I’m guessing) and it conflicts with other libraries.
I found the link to jquery and it’s instructions a little confusing and various instructions recommending porting and modifying ajaxsearch, for me the newbie

so I just wanted to keep it simple and let people know, that I didn’t touch ajaxsearch at all but instead modified the javascript that I added that was conflicting using the replace technique above. (it worked for me but no guarantees)
open your javascript file, that depends on the jQuery library that you are adding, in Notepad
Find... $
Replace all... jQuery
So again thanks to all who posted this info (save me potentially ALOT of time as I would have never figured that out on my own).