Okay, then... Can you try this?

$ strace -o 698729.out -econnect,sendto,recvfrom perl 698729.pl
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The 698729.out file should start with something similar to this:

connect(3, {sa_family=AF_FILE, path="/var/run/nscd/socket"}, 110) = -1
+ ENOENT (No such file or directory)
connect(3, {sa_family=AF_FILE, path="/var/run/nscd/socket"}, 110) = -1
+ ENOENT (No such file or directory)
connect(3, {sa_family=AF_INET, sin_port=htons(53), sin_addr=inet_addr(
+"192.168.1.1")}, 28) = 0
sendto(3, "\321\263\1\0\0\1\0\0\0\0\0\0\2my\5yahoo\3com\0\0\1\0\1"...,
+ 30, MSG_NOSIGNAL, NULL, 0) = 30
recvfrom(3, "\321\263\201\200\0\1\0\2\0\0\0\0\2my\5yahoo\3com\0\0\1"..
+., 1024, 0, {sa_family=AF_INET, sin_port=htons(53), sin_addr=inet_add
+r("192.168.1.1")}, [16]) = 80
connect(3, {sa_family=AF_INET, sin_port=htons(80), sin_addr=inet_addr(
+"216.252.123.25")}, 16) = -1 EINPROGRESS (Operation now in progress)
connect(3, {sa_family=AF_INET, sin_port=htons(80), sin_addr=inet_addr(
+"216.252.123.25")}, 16) = 0
...
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Note that 192.168.1.1 is my DNS nameserver and I don't have nscd running, so the fist ENOENT errors can be ignored. You can see that the DNS query got through since 216.252.123.25 is the IP address for my.yahoo.com and there's a connection to port 80 going on.

Hope that helps.

Update: renamed lwp-useragent.pl to OP's node ID, so it's clear where does the code come from.