Can I buy out my contract?

You can only "buy out" the contract if the contract itself says you can (that is, it has a buy out clause).
IF the contract is valid, or to the degree it is valid and enforceable (see below), if you work in violation of it, you could be sued for monetary compensation (e.g. for an amount of money reflecting what your competition has cost the employer) and/or for a court order ("injunction") barring you from working.
However, based on what you write, there is substantial reason to think the agreement cannot be enforced against you:
1) Unless you received some substantial additional payments or benefit or pay for signing the agreement, if you were fired (rather than leaving voluntarily), they can't enforce a non-compete against you. Contracts--and non-competes are contracts--require "consideration", or an exchange of things of value, to be enforceable. The consideration for your agreement to not compete was the provision of employment; if you were fired, the employer took away the consideration for your agreement to not compete, and without consideration to you, the agreement is not binding. That's why if you were fired, it would generally only be enforceable if you received something else of value, besides your job.
2) While courts will enforce non-competes, they try to strike a balance between protecting the employer and letting the employee earn a living. That means--
a) They will reduce a too-long agreement to a more reasonable length. Generally, unless you were a company owner who was paid a lot in conjuction with the noncompete (e.g. you were paid for your share of the company in one way or another), for most employeess, courts will only enforce an agreement for 6 months to 1 year; more than that is considered excessive.
b) A non-compete can't stop you from all work: only from competing against your employer. So it will only limit you from working for competitive companies (including your own, if you start your own business) who sell to the same customer base or market. If you work for a non-competiting company, you are not restricted.
c) Generally, only employees with some specialized skills or knowledge or training can be bound: if you had a very "generic" job (e.g. receptionist; benefits administrator) where nothing you do would give a new employer any competitive advantage over the former employer (even if it was a competitor; see b) above), then the agreemet might not be enforceable against you, since a court would conclude that it offers no advantage to your employer sufficient to offset your right to earn a living.