Get a big stick and go visit the ISP office
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. You are just going to have to keep calling until you get a tech that can do more than follow their script. I have talked to some that do not even know what a ping command is.
Your pingplot is great. This is a perfect example of using pingplot to show a problem. Many people post these and good "RED BAD" must fix when it is really just a issue with how the testing works.
What is key is you see massive packet loss starting at hop 2 that affects every hop in the path including the last one.
The good thing is hop2 represents the connection between your house and the ISP. This is almost always some wiring issue and it is almost always outside your house.
I will assume this is a cable connection an not dsl.
So all the standard things you check to be sure the ISP will not blame you.
First look at the modem signal levels and error logs. You should also see packet errors counts depending on the modem. Check that the signal level are within the recommended values. The exact values depend on a number of things so you are best to search for it rather than me try to replicate it here.
Since you have replaced the modem that is one thing. Next try to connect the modem to the wire at the nearest point it enters the building. You want to avoid any splitters etc. This is to preempt the script monkey at the ISP saying its the cables in your house. See if the signal level change significantly.
This means you have pretty much proved the problem is not in your house.
The tech will next try to blame pingplot because they don't understand it. What you want to do is open 2 cmd windows. Let a constant ping command run to hop 1 and hop 2. This should show the same thing as pingplot. You should see no loss to hop 1 but packet loss to hop 2. You get a tech with even half a brain they will understand that this shows that there is no problem with your pc or router and a problem with the connection coming to your house.