When you say HTML File, what do you mean exactly? Are you creating a custom theme map and modifing the SOY/FTL files or are you using an Overview page with the HTML widget or are you using Tiles?
JQuery is build into Jive so you can call using $j rather than just $, tis may solve your problem, if your using widgets/tiles though then you need to make sure that jQuery is being called correctly.
As for debugging, i use Chrome and its built in developer tools and that works perfectly for me.
If the above doesn't help please clarify exactly what steps your are doing