Can rent a center have you arrested in Delaware for non payment or do they have to take you to court

Non-payment of a debt (other than an obligation to pay imposed by a court order, such as the obligation to pay child support, or an order requiring restitution fora crime) is not a crime.  There may be harsh civil penalties for not paying a debt, such as a ruined credit rating, the garnishment of your wages, etc., but you will not be jailed for simply not paying a debt.