If you're in that bad condition, you probably need to have them removed. Ask your social worker how to get that done.
After that, you'll have a different set of problems, but the pain will be greatly reduced.
Dental insurance is not really "insurance" - it essentially amounts to a pre-paid discounted dental plan that you have to use or lose. Also, when you go to get "covered" dental work, they tack on a bunch of uncovered crap anyway to help them recover the costs of their discounting for "insurance".
You can get the same kind of discounts from a dental discount program, which are very cheap. I've found that it's often enough just to SAY you have the plan when you go in to the office, as long as you can correctly identify it by name.