What kind of health-related job can you get when you have nothing?

Nursing assistant comes to mind. Sometimes you don't have to have the CNA to do it. I didn't have one when I was an aide, and I learned on the job. Unit secretary comes to mind, too.

Where I live, nursing assistant courses are only 6 weeks long and not very expensive. It might be worth it for you to take such a course.

Other types of jobs that you might get (housekeeping, cafeteria, gift shop, etc.) won't put you on the nursing units or in contact with the patients.

Sometimes large hospitals have transporter positions. These folks go to the floor and pick up patients for x-ray or whatever.

Unit clerk or CNA might also be good ways to go.

I worked in a Group Home for Developmentally Disabled Adults before and during nursing school and I got A LOT of good experience. You pass medications, learn how to navigate MAR's, treatments, charting etc. I worked nights which actually gave me a lot of time to study.
We had residents with g-tubes and straight cathing, also CPR and first aid. Honestly, I can't think of a better preparation for nursing. Also, if you are low on your finances (I sure was) you get your meals at the Group Home and also get some entertainment paid for when you take your residents out in the community for recreational activities, such as movies, concerts etc.

Definitely check it out! They tend to train you on the job and the medication administration course was paid training as well. You won't get rich, but the experience will make you wealthy!