I think the ISP in question might have some DNS caching system. Your host, during the billing system fiasco, probably resolved your domain name to a different address. This DNS resolution was picked up by other DNS servers, and possibly cached for a certain amount of time. There are a few possibilities:
1) Wait. After a certain amount of time, the DNS cache will expire, and the ISP's DNS servers will query one of the main DNS servers in the world, and they will have the updated information.
2) Contact your web host and explain the problem. Perhaps they have dealt with this before and know a way to fix it. The billing and IT departments don't always talk to each other in cases like this, because the non-techies in billing don't know about DNS resolution (no should they, and still be working in billing).
3) Contact the ISP and ask them if they implement DNS caching, how often the cache expires, and if you can request a certain domain name be expired manually.