I'll just join in here : there are no problems using jQuery with DNN.  You should convert the scripts using $() to jQuery() for better compatibility with the existing DNN scripts, but apart from that there should be no problem at all.

A lot of the problems with this type of thing is incorrect referencing of external files, or incorrect ordering of libraries (jquery library has to come before references to it).  It's a good idea to check to make sure the relevant js and css files are being downloaded, by using the 'Net' panel of Firebug.

With jQuery, you should have very few problems between IE, Firefox, Chrome and others.