The military isn't really picky about where your bachelor's degree comes from (as long as it's credentialed), or what it's in (there are some career fields where they require specific majors, but even some of the more technically-oriented jobs don't have any such requirement). It's really just a check in the block. If you have nothing else on your resume, then you probably need something better than a BA in underwater basket weaving from the University of Pheonix, but in your case you could get exactly that degree and then go to an officer recruiter and leverage the rest of your resume to find an appropriate career field.
If you had a high school diploma, you'd still have lots of good opportunities. Most of the truly technical jobs in the military are performed by enlisted personnel. Some officer jobs are relatively technical (engineers and other acquisition-related career fields, aviators, nuclear power officers, etc.), but all officers are expected to be leaders first and foremost. Even officers in technical-sounding career fields (e.g. cryptology) serve primarily in a leadership/managerial/administrative role, with the enlisted personnel under them performing the hands-on work. In the early days of computers, all of the computer programmers in the Navy were enlisted, because their job title included the phrase "technician," and officers don't serve as technicians, enlisted men do. Lately there has been a realization that some technical jobs require a level of knowledge that most high school graduates simply don't possess, and so the Navy recently established a new officer designator for hackers: http://www.informationwarriors.net/showthread.php?t=623
An interesting thing about this designator is that it still preserves the idea that officers are supposed to be leaders, via a very unique and unusual mechanism: any officer with this designator must, after five years, either change designators or leave the Navy. I'm willing to bet that this requirement is based on the idea that this isn't really a leadership job, and that they're willing to have very junior officers in non-leadership positions, but that after a certain point they want them to shift their focus to leadership like all other officers.