1) Start with the given:
CUTE PURPLE DINOSAUR

2) Change all U's to V's (which is proper Latin anyway):
CVTE PVRPLE DINOSAVR

3) Extract all Roman Numerals:
C  V    V  L    D  I   V

4) Convert into Arabic values:
100  5   5  50   500  1    5

5) Add all the numbers:
666

Thus, Barney is Satan.