while the dome is just a weather cover, 'whether' you can still use the unit is suspect, as the weather may have not treated it well, but you may also find that it's no longer supported and replacing it with a $250 DISH Playmaker, or $350 KING Tailgater, might be just as easy.
As for the receiver, that's actually the 'brains' of the system, and what you'll need to make any antenna work - the antenna is simply what 'captures' the signal, the receiver processes it and sends it's output to your TV. The receiver is what Dish or Direct is actually charging you monthly for.
A simple Dish antenna, like either of the one's mentioned above, with a simple Dish receiver will serve you well. They are portable, and can be placed anywhere to pick up the satellites, or can be mounted, whether permanently or temporarily, on your roof. Ours is at the rear of the roof, right near the ladder, where I can allow it to travel with us, use it anytime we are parked, or easily detach it and bring it down to the ground, if needed.(or somewhere else on the roof, for that matter).
Running coax cables from the antenna to your receiver is generally the main question most folks have who are new to RVing and Satellite service. Running coax, though, is simple. You can try to use existing coax connections provided by the original builder, but sometimes these are just out-of-date, or have splitters in-line, which don't work well with two-way Antenna systems, which require power thru the coax line.
Use slide seals for coax entry into the coach, or plumbing vents, or windows, or even existing cable, plumbing, and electrical runs that already exists.
...2014 Ameri lite 259BH...
towed by our '14 Thor Palazzo 33.3 diesel pusher...