Bad IP or bad modem?

Last week changed from Time Warner Road Runner to Verizon DSL. Verizon informed us we were "good to go" connected the Modem, ethernet and phone jack filter, modem lit up for power, dsl, and ethernet but not internet. The house telephone also didnt work. Requested a service man come, he came Saturday spent all of ten minutes and everything was working great. Two hours later we kept getting kicked off the internet and when we try to reconnect we get a message saying can be found. We called Verizon they said try unplugging and re plugging the power source to the modem. This fixed it, for fifteen minutes. It has gone on like this for the better part of the week. Called Verizon again last night and they say everything is good on there end, our internet light on the modem does stay lit with occassional "pulses". I tried to release/renew IP config. after Windows 7 suggested it, got a message saying our IP address was invalid. PLEASE OFFER Suggestions in very basic language as I have no technical ability and Verizon says if they send someone out again it will cost us.
 
First, every device connected to any phone wall outlet *MUST* have a filter (except the modem itself).
Verizon should have installed them but perhaps overlooked.
 
OK - - disconnect the telephone altogether, Power Off/On the modem and see how long you keep the connection.
That filter may be bad.
 
HI, have you completely reset both the modem and the router?

as in a hardware reset.... pressing the reset button on both....
 
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