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How can I stop JQuery import from breaking existing code

I'm a beginner developer in Html/Javascript/CSS/Jquery coding
and while working a project, I had to integrate Jquery with previous code.
As soon as I imported Jquery, even simple buttons became styled badly. Jquery worked fine as long as I used its classes to assign styles to objects.
However since the rest of the project is not to change style, I need to know what I'm doing wrong. I've checked the objects for classes, and they have no classes, so it's not a css issue.
I narrowed down the error to the following screenshot, but I still can't figure it out. It seems to be something simple that I missed but I have no idea what it is.
Ignore the class="ui-content" and class="ui-button-text". I was just testing if something would change (nothing changed).

Try to inspect the elements that are styled wrong with your developer tools in the browser. The only styling in your example is in jquery.mobile-1.4.5.min.css, so that's where I'd be looking. Did you mistakenly delete a link tag to your stylesheet?

JQuery carousel and template doesn't work together

First of all, I'm sorry if this is already asked. I couldn't find a answer.
I have a HTML5 template bought at themeforest and a jQuery carousel. I am not very similar with JavaScript or JQuery.
When I wanted to implement the carousel like it said in the description the JQuery/Javascript didn't work.
I found out that it could be the version of JQuery. The template(cleanstart) uses version 1.11.2 and the carousel uses 1.44.4. When I changed the carousel to that version it didn't work. When I changed the template version to 1.44.4, it didn't work either.
Then I've put the text from the carousel.js in a script tag in the HTML, and that seemed to work but then the templates jQuery didn't work...
Do you have any idea what the problem can be? Maybe a variable with the same name? I really don't know how to solve it.
Help is much appreciated!

With just this Information, It's pretty hard to help you. It could be a problem with your Implementation, a compatibility Issue or many things else.
Do you have a public page where the template and the carousel are implemented? Does the console window give you any error (if you don't have it yet, I recomend you to get Firefox and the addons Firebug and Webdeveloper Toolbar).

I have found my problem. it was a scroll section that causes the other jquery to stop. When I removed that part of the code, nothing bad with the carousel happened and the other parts worked fine!

Tooltip with Bootstrap not Styled as is shown in example?

I have tried using the example code that is provided by the Twitter Bootstrap docs,
Hover over me
and although I do get the hover over effect, it doesn't look like the pretty version that bootstrap provides. I have tried looking this up in Google and Stack Overflow, but most of them offer solutions on how to customize the look of the tooltip. I would just like to use the default look bootstrap provides.
Any thoughts on why mine may be looking like the screenshot below?

Clear your cache.
Make sure bootstrap.min.css file reference is not broken or other files.
Go to your dev tool and verify if there are specifics errors we can go over.
Make a prototype using the same conditions as your example so that you can identify your
problem clearly.

Use this. Also check using inspect element that your customised classes are not overriding the default CSS.
<a class="btn btn-default" data-toggle="tooltip" data-placement="left" title="first tooltip" data-original-title="first tooltip">Hover over me</a>

also make sure you are adding the correct bootstrap css and javascript seems like either you don't have them or their path is wrong

Get a style switcher like on themeforest

I would like to add a style switcher to my site and I like the ones used on themeforest templates.. How is that done and what library are they using?
Example: http://centum.envato.tabvn.com/demo.php
Slides in from the left side.
I use drupal so I'm hoping there is a module but I couldn't find anything like it.
Any ideas?
WHY AM I GETTINGS VOTED DOWN? PLEASE EXPLAIN IF I'VE DONE SOMETHING WRONG HERE

This is fairly easy to create yourself just by adding classes with an onClick handler, and then styling with the classes how you see fit. They're probably not using a plugin for this but is actually a bespoke function they've created them selves with the jQuery library.
For example.
$('.style').on('click',function(){
$('.itemToChange').addClass('styleOne');
});
Please see a basic example with this Fiddle.
Please note this is a VERY basic version, and the example you show is much more indepth

if someone still looking here are two solutions
Blast.js or
JTS

The example you provided is using this
http://drupal.org/project/flexslider
EDIT
I'm sorry I got confused.
The style switcher is custom made by Envato, the company behind themeforest you can find the code here
http://centum.envato.tabvn.com/sites/all/themes/centum/js/switcher.js

Cant get Bootstrap modal.js to work

EDIT: Keep in mind this answer was asked before Bootstrap 2 came out and therefore is relative to the first release
I am trying to dynamically add and show Bootstrap modal windows with AJAX content, but after looking at the documentation for a good hour and a half I dont understand what classes or attributes I need to add to my modal div so they work with the modal API.
Right now I have something like this:
var $modalWindow = $('<div />', {
class: 'modal fade static',
style: "display: none;",
text: "Test"
});
$('body').append($modalWindow);
$modalWindow.modal('show');
And it doesnt work... Maybe I am being dense, but I cannot find any info on the docs about how to setup my modal window before calling the show method.
Edit: Fixed it, apparently bootstrap-modal.js requires bootstrap-tipsy.js and bootstrap-popover.js, although it is not mentioned anywhere in the documentation. Seriously, Bootstrap has the worst documentation, specially considering how popular it is.

Fixed it, apparently bootstrap-modal.js requires bootstrap-tipsy.js and bootstrap-popover.js, although it is not mentioned anywhere in the documentation. Seriously, Bootstrap has the worst documentation, specially considering how popular it is.
EDIT: Before downvoting this answer, consider this was before bootstrap 2, and as another commenter said he had the exact same issue and also solved it by adding tipsy and popover.
Boostrap 2 is way better than its first incarnation, BTW