This could be any one of a large number of things, starting with a wiring fault in the battery terminals that is not powering up some or all of the motherboard, right up to a motherboard that is fried. You could start by disassembling it and seeing if you can find any obvious fixable hardware faults.
iFixit has a really good writeup of the innards of the Note 4 - it is overall one of the easier phones to maintain. Some of the components are held together with adhesive but it's nowhere near as bad as most.
https://www.ifixit.com/Teardown/Sams...Teardown/34359
Short of starting to replace components in an attempt to fix it, if you cannot find any obvious hardware faults it's probably a goner.