Ok but you have tried every thing else if I remember correctly you have set up port forward, UPnP, Disabled your firewalls you connection says it is not firewalled.Adjusted your connection settings, LimeWire works on your work laptop using the same connection. The problem has to be a program on the machine your connection seems to be fine since your work laptop works.

I did see that Connect Protect does block P2P but you said it is configured to allow limewire have you tried there support site.

Any way it is way past my bed time so I will sign off for now 1:10 AM have a good day.

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A little common sense goes a long way

Later Grandpa