I guarantee that you have not been able to ignore advertising or cause it to have the opposite influence. You're fooling yourself.
Oh good, a chance for some fun.
What kind of computer do you use? What kind of portable media player? I guarantee that you chose them because of advertising. You know which components to buy when you build a computer because of advertising. You know which cereal to buy because of advertising.
The only computer I have is the laptop my company brought me. I don't have a portable media player. I don't buy cereal.
Even if you buy the cheap store-brand of corn flakes, it's because the store-brand is piggy-backing off the effect that Kellogs' advertising had on you or you wouldn't even know to buy corn flakes.
The ingredients I buy and the dishes I cook would not surprise a 16th century peasant, save for fruits like oranges and bananas. You're right, I don't know to buy corn flakes, because I have no idea what value they'd give me. I do know that I'm in no worse shape than people I know who eat corn flakes. Actually, the last reference to corn flakes I remember is them being dismissed by someone in Roald Dahl's story "Charlie and the Chocolate Factory". I do see ads sometimes, but I couldn't actually describe a single one I've seen.
I bet you know the names of Apple's laptop computers. I bet you know the names of the individual programs in Adobe's Creative Suite. I bet you can tell me the names of car models made by the biggest car companies. All because of advertising.
You're right, I do, but only because that's what my company bought me and I dug around on the Debian wiki on how to install it on various Apple laptops. I haven't the faintest clue what Creative Suite even is. I'm notoriously bad with car models, though I know a couple of 60s brands and could tell you a couple of models that my friends have, but I couldn't actually match them up to a picture. Except perhaps the Mini, which I saw on Top Gear.
There's a long game in advertising too. Even if you aren't directly influenced to run out and buy a product, you learn the names, you learn the qualities that made one brand better than another. Eventually you will make a decision, and though you think you're making the decision based only upon your own independent thinking, the marketing plays a bigger role than you think.
Actually, I don't have time to pay attention to ads. Most on the Web are blocked and I don't watch television. I subconsciously ignore billboards. When I buy products, and I don't buy many (before you go on about shampoo, body wash and shaving cream brands, I just use soap for them all), I either go by price (as with toothpaste), habit (as with Old Spice deodorant because my grandfather used it) or developed taste (as with alcohol). Now, I'm not your typical consumer as I'm poor and spend extremely little, and that almost all second-hand. I did buy a refurbished ThinkPad once, largely on the reputation it had amongst my friends -- whether that was due to advertising, I don't know, but it held up much better for me than Dell laptops I've used.