IP address yes, DNS no

In the process of migrating website hosting locally, changing ISP. I can find our site by using the local IP address, but not the ISP assigned address, nor URL. Name resolution is deemed successful via Optasoft shareware. The ISP is propogating the web with our new information currently, but as of this morning we could still use the ISP assigned IP address. Now, no go. Any thoughts or suggestions?
Thanks