"This network only provides broadband Internet access and has no connection to the corporate net, other than through the PC."
What do you mean "other than through the PC"? I mean, that's really the whole issue. A PC is just a few clicks away from becoming a router. You're network path used to look like this:
Internet<->Firewall<->Proxy<->Notebook
Now it looks like this:
Internet<->Firewall<->Proxy<->Notebook<->Wireless<->NAT gateway<->Internet
Because of mobility, notebooks often present other challenges as well. IME, they are not patched as timely as regular workstations. They are used away from work and in hostile environments, like hotels and airports, and tend to get infected with malware more frequently (i.e. surfing higher risk sites when I'm at the hotel...porn).
If I gain access to the wireless network, I would typically have unfiltered access to any nodes on the wireless network. In your scenario, that includes those higher risk notebooks which are also directly connected to your internal network (i.e. I completely bypasses all those carefully implemented firewalls and proxy servers you mention). If I can compromise one of those hosts, then I will likely have full network access to your internal network.
