I got a psychology degree and also languished for ~8 years afterwards.
Then I applied to a 2 year MBA program at my local state university and paid for it out-of-pocket. At year 1.5, I was recruited into a job with a 50% pay raise. Now, 8 years later, I earn double what I used to (which is still underperforming many of my peers, but so be it. I work 40 hour weeks and set my own agenda.).
Lessons:
-Why get just another bachelor's? You can often leverage your semi-unrelated degree into a master's program that takes the same amount of time at a similar cost.
-A "career" is a job you've done for 5 years. I've had about three of them. At 36, you might have 3 left to go.
-In hindsight, some more technology electives or the MIS program would have served me better.
I don't care much which job I'll be doing.
I think you care and what you're saying is "I'm flexible". You also probably have some talents or interests you could leverage at work.
I'm also not a very competitive person, do you need to be competitive for managing?
Nope. To manage you need to be cooperative when it matters and firm when it matters. It's an art more akin to dancing or figure skating than the conflict-based plots we see on TV. The key trait you need to be a leader is diligence. That is, an unblinking fascination and interest in the work that motivates you to stay late to balance reports and write quality improvement plans. That person is getting the manager position, regardless of everything else. If you're not that person, consider the multiple other options.
Why focus on managing? Oftentimes, it is easier to obtain good paying work as a skilled contributor. E.g. nurse, programmer, specialist, technician, analyst, etc. For any of these roles, there might be 10 contributor positions for every 1 manager position. That means less unemployment time and more FU options.
Also, MMM did a write up on 50 jobs paying $50k without a college degree:
http://www.mrmoneymustache.com/2013/07/25/50-jobs-over-50000-without-a-degree-part-1/ Perhaps this will help identify some options.