Many DSL problems actually stem from the provider's use of PPPoE and the need to tune maximum transmission unit (MTU) size. I haven't encountered your problem before, but suggest searching the Verizon Online DSL FAQ and related user forums for anyone who encountered this same scenario.
If you haven't done so already, you should also verify that the laptop and PC can communicate with each other locally on the LAN, without using the DSL uplink to the Internet, to eliminate any local sources of interference (for example, duplicate/conflicting private IP addresses).
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