Arduino Mega 2560 - TFT 3.5 Display is not working with libraries suggested
I have the same display. It has ILI9137 chip using 8-bit mode, so original Henning Karlsen UTF library doesn't work. You can find this library patched to support this display using Arduino MEGA at https://github.com/dgolda/UTFT

If display wouldn't work it is probably broken. I've received first piece broken - only backlight was working, but second and third was OK.