If it had a shallow well pump before it should be able to handle another. Getting the pump primed again can be a challenge though. I have a dug well and it's 275 feet from the house, with no vertical lift. When I replaced my pump I had to take the foot valve off, then pump water from a bucket backwards up to the spring.
Is it a drilled or dug well?
Don't leave the water lines open, that's one reason it isn't building pressure. Let it build as far as it will go, then crack one faucet until the pressure starts to drop again. It does sound like you have air someplace but unless there's a leak unrelated to the pump failure; either in the line, foot valve or pitless adapter; you should be able to bleed it out.