You owe 2700.00 for past child support and you are going to court for it you had a job that barely got you buy and tried to pay but couldnt. You are not trying to avoid just couldn't pay. What happens?

Don't try to duck or avoid the authorities, on something like this. Be upfront (and civil) with them, and have copies of your recent paystubs, tax forms, and bills and expenses (regular and unexpected) ready to show. You might need to engage a lawyer... which of course costs more money.