The PING might not be conclusive, and awful lot of routers and firewalls block ICMP packets
Against established good practise, yes. But I thought advising to use "nmap -P0" might have been a bit overkill
If the DHCP server on the network he is trying to join is working properly, it should provide the correct default gateway address for him, as well as DNS server addresses,
Not a given by any means. I take you're not a sysadmin / never configured a DHCP server?
that address is a bit unusual for a default gateway, which is usually x.x.x.254
A gateway is just a computer which allows you to talk to a different network. It could be any valid non-broadcast address whatsoever, as long as it's within a network you are connected to.
I think you're assuming a standard wireless home ADSL router setup. He might well be trying to connect to his corporate net.
Further advice: try a wired connection and see if it works.