Contact the network, then. If your IP *is* changing whenver you reconnect to the internet, then it shouldn't always be blocked for too many hosts. You should be able to disconnect from the internet (not IRC) and reconnect and then get on the network. If you cannot, then the network may be consindering an entire range of IPs as being the same host. Best to contact them and explain the situation and see what they can offer you.
Otherwise, you may need to just use another network and save yourself the headache.
