i think some guys in this thread have already given great answers. as mentioned above, punk has been co-opted and commercialized to neuter any real threat it could represent today.
punk is about standing up to the system and telling it to go fuck itself. the look is secondary. you need the attitude. not everyone originally had the actual attitude, but ran with the look, just like labeling yourself with an -ist allows you to fall into a clear box without having to put work towards it.
the system (i.e. the cultural zeitgeist) isn't the same as it was back then. on the surface, non-conformity is encouraged. self-expression at almost any cost, individuality, and personal freedom in some aspects are now seen as universal values, and propagated as ideal to aspire to. we are approaching full relativism.
but what are the things that you're not supposed to speak against today? which values are you not supposed to adopt? if you want to "be" punk, those are your targets. if you're uncomfortable with the answer to that question, then the system aligns with you; why go against it?
if you want to "look" punk, really punk, then you can buy the diluted, ingested look of punk which is already being sold to you. that niche has been catered to. or, you can push it to the authentic extreme, and look unfit for society. there are many ways to do that that aren't tainted by the cultural heritage of punk. but it can be done within that tradition as well if you want to push it, because no matter how many documentaries people have seen about how cool stinky beer-and-spit-covered concerts behind chicken feet, there are things that just can't pass.
if you can stomach the projection of the unapproachable in your appearance, then that's a way to internalise the new punk. but the look is just the surface. it's signaling. you can be punk without forcing yourself into a box that we've inherited from several decades ago.