What is this military turboprop aircraft?
From that really grainy, blurry picture, it looks like a C130 Hercules.

bulbous fuselage
Straight, ironing board-like wings
High wing configuration
4 turboprop engines
Huge, high empennage
The rear is shaped like it could have a ramp.

If you are sure it was a turboprop, it looks like the C130 is a strong contender.