PS4 controller keeps disconnecting
If you verified that your old controller works fine, its most likely your new ps4 controller. Another possible test you can do it try it on another PS4 system at a friends home.
Since you purchased from Amazon, you might have a defective ps4 controller. You can just do a no hassle return with amazon and get another one. Go here to amazon returns here: https://www.amazon.com/gp/orc/returns/homepage.html