Hi Fredrick,

The LM317 package would be rated at 1.5A with a very good heat-sink and the correct input voltage, to avoid, dropping too much voltage and heating itself.
(input – output differential V)
http://cache.national.com/ds/LM/LM117.pdf

With no heat sink, 15 V input 5 V output, the 317 could overheat with just over 200 mA at 25 C.

Regulator Heatsink Calculator
http://www.ef-uk.net/data/heatsinking.htm

How much current does the OLED LCD display draw?

Is the voltage regulator getting hot (to your touch)?
Can you “oscilloscope” the +5V supply? Watch for the voltage to dropout.

-Adam-