Why Does My Computer Work When My Phone Service Is Dead ?

If you mean you have a landline phone or phones and your service has been disconnected, the phone/internet companies sometimes don't cut the internet connection off at the same time. They can still run it and sometimes leave it running for a few weeks after cutting phone service. But, if your payments are all caught up, and you want and are paying for service to your phones and aren't receiving it, then you should call your phone company about it as that sounds like a problem.

If you mean that your internet works on your computer but not on your phones, that sounds like a router problem, if they are connected via a router. Which you may need to reset your router and disconnect your phones and reconnect them to it.