My university has blocked the Gnutella port, so I am unable to get connected to LimeWire. I was given a list of alternate ports, of which I have tried numerous and none have worked. I don't know if I am doing something wrong. Also, how is LimeWire supposed to "know" that I'm not using the Gnutella port? Wouldn't it continually look for that port and then quit trying when it's not available? If so, how am I supposed to alert the software to the port change? Any advice on how to connect would be helpful...Any step by step directions would be helpful as I consider myself to be relatively computer illiterate.

When first dlding and installing LW, it is set to listen to (that is, to try and connect via) a default port. If you change that port through LW's Options (located under Tools), then LW will try to connect though the new port. It doesn't matter what port it used to listen to.
Where did you try the new ports? In LW? Are you sure you clicked Apply after changing it?

PS: what is this doing in "New Requests"?

__________________
iMac G4 OSX 10.3.9
RAM 256MB
LW 4.10.5 Basic
ADSL anything from 3 to 8Mbps/around 1024kbps

"Raise your can of Beer on high
And seal your fate forever
Our best years have passed us by
The Golden Age Of Leather"
-Blue Öyster Cult-