Your vote is not the only political power you have. You can organize people, even if it is only at the local level. Once you do that, you have begun to gain political power, and that is how political careers are started. We do not have titles of nobility here; nobody is more entitled to be politically engaged than anyone else.
In practice, it is hard to take power from the established parties. It is hard to get past the local level without being well-connected. Hard, but not impossible.
Organizing people isn't the only power you have beyond your vote, either. Issues are complex, and I feel like I couldn't reasonably vote FOR something I want without also voting against many things I want. I could spend countless hours tracking down the candidates who, on average, best served my personal interests and preferences, all so I could cast my one little vote...but that wouldn't make much sense for me. There are better ways to spend the time.
If you care about animal rights, you can spend that time volunteering or making more money to donate to DIRECTLY support the causes you care about. You can pay closer attention to the dollar votes you're casting (which can't be discounted as a means of political influence).
If you're bothered by GMOs and factory farming, you can help set up local gardens to reduce reliance on conventional produce. You can educate people around you so they understand why it's important to maintain the integrity of our food supply.
If you don't appreciate companies turning over your information to the government, you can (try to) find one that doesn't, and let the company you're leaving know why. You can donate to the EFF and similar organizations.
As much as people like to get emotional about voting, it's not terribly effective as a means of bringing about change - especially once you take into account that politicians often mislead people about their intentions or change them completely once they have more power.
In practice, it is hard to take power from the established parties. It is hard to get past the local level without being well-connected. Hard, but not impossible.