What should i start doing?

To make a long story short.

Due to me being sick, uninsured, and just plain bad luck for the past 4 years, i had to put hospital bills and medicines on credit cards, they were all closed when i was on a consolidation program i had to get off of due to be being unemployed and i couldn't afford to pay for it, now i cannot go back with most of the cards that i really preferred to be on the program, so i just pay 4 or the 6 cards (two are on programs with the company) higher then the minimum payments.

I have a best buy card that one of the zero financing will end this month unless i pay $352, but lately, since i had these closed account for such a long time i really want to start paying them off card by card. ( if you are wondering why i used my card it's b/c my computer of 4 years just died on me and no matter who saw it/ looked at it nothing was working, and i need my computer to pay bills and school)

So here is my question: Should i pay the $352 so i can continue getting zero financing for my other purchases or just put higher amounts of money lets say like $200+ on my lowest closed card and do that every pay day until each and every one is paid off while paying a little higher than the minimums with my open cards? Or i should just pay the $352 this month and just start paying down my cards next month since i am done paying for car insurance for maybe the next 2 months until it comes back up again?

Thank you!