Difficult to say. The military is downsizing. Even the NG. So they are recruiting less, including less prior service people. Talk to the recruiter and explain the circumstances. You can also seek to upgrade the discharge and change the re code.
email@example.com 703-298-9562, 800-401-1583. Answering your question does not create an attorney-client relationship.
It is unlikely you can reenlist with a prior General Discharge. Filing an appeal of your discharge type with the Army Discharge Review Board may be an option in your case. Discharge upgrades are realistic and an experienced attorney can help put together a strong package.
Andrew Cherkasky of Cherkasky Law, LLC is an Illinois attorney focused on the representation of military members and veterans. The advice given does not form an attorney-client relationship. Please call anytime with questions: 703-314-6475