Is your LW connection ok? How many green connection bars do you see?
I see only one green Bar
1. OS version? (eg: Windows 98)
Windows XP
2. What firewalls you have?
Not sure whether it is turned on
3. How much ram?
0.99 GB of Ram
4. Hard Disk space available?
10.4 GB
5. Connection type? (eg: dialup, broadband, cable, etc.)
I am using the same software at home through broadband and getting results pretty quickly.But at my office it is pretty slow and no search results displayed.

6. Modem & router brand name & model numbers?
Not sure
7. Where are you trying to connect from (house, appartment complex, school, student accomodation, work, etc.)?
From work place
8. What version of LimeWire (LW) & Java do you have? (Go to LW's menu Help>About LW...) Will show both LW & Java version.
4.13.2
Java 1.5.0_11

9. Who is your ISP provider (Internet Service Provider)?
It seems to be a proxy not sure how do i find
10. Do this simple test for us. Using your browser go here: http://www3.limewire.com:6346/ The page should say 'Your test worked!'. What happens when you go there?
It shows the static test as mentioned by you 'Your test worked!'.
11. Are you sharing the connection with other computers or p2p sharing programs? If yes, please give details of set up.
No
12. Is this a your 1st try at LW or is this a new problem with an experienced user.
Only at work place
13. Do you see a brick wall in front of the blue world icon at the bottom of LW's interface
I see the brick wall mentioned by you