You probably have your old pay pal account listed as the preferred payment on the Chess.com account. You probably need to go into your chess.com account and change information to new account... would be my quess.. ?
How can I change my previous paypal account?

To change your chess.com payment preference...
Put cursor on Home, then click ACCOUNT
go down to account purchases and history.... click it...
then directly below (in red text)... click here to update your billing information
then change your payment method...
I can't pay via my new paypal account, because my old paypal account used by chess.com or something? Please help.