OK, let's start with some basic information.

1) You are sending an ICMP datagram thus a TCP port is not going to respond. Get the port idea out of your head.
2) There is no good reason to ping a broadcast address unless you want to initiate a smurf style attack
3) WTF are you doing this for?

I would have thought that it would have been more like nmap -sS -vv -n -p80 -P0 192.168.1.0/24 sent out over the network rather than the broadcast to get all hosts to respond to a probe of port 80.

Perhaps someone should get TH13's opinion?
This is the sensible way to do local subnet discovery w/o flooding the piss out of the network.

What are the devices on the network? Generally using ping 192.168.1.255 -t (windows) or ping 192.168.1.255 -b (linux) should work unless ping is surpressed by router/switch/firewall.
This will make every host on the local subnet respond until you stop the ICMP request. You will more than likely see a DUP! message appended signifying multiple responses to the request.

I'm going with MsMitts in that something is eating the ICMP broadcast request. I would check into what is actually sitting on your LAN.

What I find stranage also is doing a nmap -sU -p42508 -P0 -S 192.168.1.18 -vv 255.255.255.255 only return me one host. This, I don't understand at all.
See above datagram statement.

Also nmap -vv -sP 192.168.1.0/24 will return all live hosts along with MAC and manufacturer of the NIC. This is the correct way to get info on hosts on your subnet.

Again, what are you trying to do?