What tier did you pgrade to? The only ones that should require a new router are 100Mbit and up download speeds.
Have you tried connecting the old router instead of the new one? It should still work even if you are a 150 Mbit user. When you do that do you still have the same problem. If yes then point out to Verizon tech support that the issue only started when the upgraded your tier (I'm presuming you had no issue before?). If no then report to Verizon that the new router they shipped you is apparently defective.
Are you connected to the router by ethernet or wireless?
I upgraded to the 75 and I was so excited when I read you post. I ran and got the old router and plugged it in but the internet light stayed orange. This is the second router they have brought since the upgrade.