How do I find out it is hd44780 compliant?
The lcd datasheet provides a link to the controller datasheet. You can compare the commands there vs. those in the hd44780.
What is the regular code, where?
The code used to drive a regular hd44780 display.
I am fairly new to this and the only thing that I know it is that Newhaven has an initialization set up that is written for an 8051 (does not work with Arduino).
The device doesn't care if the signal is sent from a 8051/arduino/any other beasts, as long as they are the right waveform.
Do you mean regular initialization code for Arduino or the NT7605 controller?
Coding to a datasheet is fairly easy, as long as you understand the datasheet.
In this case, you need to make sure that the power is up; you have the right contrast; and then worry about the code.
Your code has numerous places that can be improved upon.
But now, you need to make sure that the device is powered up correctly and you have the contrast.
If you need a way to generate negative voltage, net me know.