AFAIK Verizon does not block p2p sharing.
Start here: If LW Will Not Connect (click on the blue link)

I believe CenturyLink may be blocking as well. Last week I had no problem using LW5. Past couple of day though I start LW and it will connect (mostly with only a med connection now) but it will not download anything and when it tries it is at like 2 or 4kb/sec. Mostly it goes through the list of connections then shows a failed download or a stalled one.

Hp DV5217cl laptop
2gb ram
Win XP Pro SP3
AMD Turion 64
DSL Connection

Would love if anyone could confirm this

From Century Link's TOS: H. You will not run programs or servers that provide services to others through the Services which includes
web hosting, multi-user interactive forums, game servers, operating an internal mail/http/ftp/irc/dhcp server
for external connections or supporting multi-user forums, or engage in excessive peer-to-peer file sharing
activities

So I guess the question is what do they consider excessive. They also monitor activity from your pc.