Hi Andy,
The default "Blink" sketch built into the Arduino IDE blinks the LED on pin 13 of the Arduino Nano, not the TFT screen. I'll take a stab and figuring out the white screen stuff tonight and will report back if I figure out a software-based fix.
In the mean time, since you can upload code, can you try uploading either Ashhar's master branch, or my pdq_gfx_update branch? In my experience, after uploading new code, the arduino resets and then the screen works.
Reed