If I cancel my landline phone service, will I still have internet access?

If you ported your AT&T number, then AT&T closed the phone account on your behalf and I would expect that any open technical issues would get closed.

That's a question for customer service to see what's available in your area and what service you currently have. You say landline, is it a stand-alone traditional landline or is it digital service where the phone plugs into a modem? What's your Internet service?

Traditional landline.  AT&T confirmed that I will NOT lose Internet access (via Earthlink).

I will cancel my AT&T phone-service on Thursday morning

Unless your internet service is DSL thru your AT&T landline.

The AT&T chat-agent said: "Let me quickly go ahead and pul up the details of your account".

Then she said: "You can access the internet service without landline service".

Ok. That's good to know then. Do you have DSL internet?

Doesn't sound like it the OP stated they had Earthlink

You should be able to have "dry loop" DSL with Earthlink.  But I wouldn't be very surprised if gets cut off and you have to work to get it back.

Earthlink said my DSL internet service will not be cut-off when I cancel my AT&T landline service.  My DSL requires a dummy (non-active) phone jack.

@OttoPylot & @JefferMC Would the OP still have AT&T landline and use a CLEC for DSL? The only CLECs I delt with had both phone and DSL service not split with the local carrier.