Ok I will explain this as basically as I can, please read carefully.

I have 2 computers on my network. They are both connected to a Router, which is connected to a DSL modem.

Computer 1 is running Limewire.

Computer 2 is mine.

When computer 1 is running Limewire it is CONSTANTLY SENDING HUNDREDS of packets to my computer 2 on port 137 which gets blocked because of my software firewall. If Limewire is quit on computer 1 then computer 2 stops recieving the traffic.

Why is Limewire on computer 1 flooding port 137 on computer 2??? COULD SOMEONE PLEASE TELL ME I should not be recieving ANY traffic from the other computer, this DOES NOT make sense.

Your router is not configured properly.
Contact your DSL tech help.
Try connecting only one computer to your router at a time and observe the results.
Check your IP adresses
if xp
Start > run > type CMD
type "Pconfig" at command prompt.
writ doen the results and compare on both computers.
IP addresses must be diffferent.

What is your operating system ?
Decribe your computer. Brand, Speed, How much RAM ?
Need more info and history about your computer and the problem.