Dispatched with the Area Navigation System inoperative; a DHC-8 flight crew experienced multiple failures of ATC to recognize their /A [slant alpha] status and were given a direct route clearance they were unable to fly due to being below the MRA for the 200 NM leg.

Narrative

We were operating with the RNAV MEL'd; filed from our departure airport via XXX YYY ZZZ to our destination. The Captain checked the flight plan and route flight against release and enroute charts and I advised ATC that aircraft was /A [slant alpha] equipped (no RNAV). Multiple times during flight we were told to proceed direct to [a waypoint] and we had to advise ATC we were unable. After crossing YYY and turning to ZZZ we had no course guidance as we were outside the service area of the ZZZ VOR and there are no published airways from YYY to ZZZ. We advised ATC we were unable to obtain course guidance. We were given a heading of 055; then direct when able. We flew that heading with no knowledge how far we were from YYY; what the winds were; or time to station. Situational awareness was significantly degraded due to no navigational references. Dispatch didn't change release to reflect the MEL. ATC didn't check to see if we were RNAV capable. [We the] flight crew [were] unsure about the service capabilities of VORs. We should check routes to make sure navigation can be maintained throughout flight.