Addicted and highly dependent on nicotine. Does the patch work?

Yes. Using nicotine patches when you stop smoking increases the odds that you will succeed.
Nicotine patch. Works when you are motivated to stop, and you select an adequate patch. Most suggest a 21 mg patch for two packs a day use, 14mg for one to one and a half packs a day, and 7mg for less tan a pack. A few need two patches for more than two packs a day. Taper to the next lowest patch after four weeks, and stay on the 7 mg patch for 6 weeks. No smoking or gum when on the patch unless directed.