Please confirm that you mean you have no service at all? Voice, SMS & data?
Roaming might be active on your account but has the phone got it switched on?
Also find the option in your phone to list the available networks? You should be able to list them even if you cannot roam onto them. The USA uses differing frequency bands to Europe for mobile networks. If no networks are listed it might be that your phone is not capable of working in the USA or the capability is switched off. That said most modern phones are capable of using some subset of the USA frequency bands. So you should be able to list and connect to at least some of the NY networks but probably not all.