I think a MAP sensor problem is very possible. If the vacuum line was disconnected, it would read atmospheric pressure, not vacuum. Atmospheric pressure (or near to it) usually only happens at wide-open throttle, so it could think the throttle is all the way down, meaning it'll be expecting a heap of air thus dumping in a heap of fuel. Assuming the MAP sensor itself is working. It could maybe just be faulty and doing the same thing (with the vac lines being OK)
Maybe find the map sensor, take off the hose, and put a vacuum gauge on it. It should show vacuum. If no change, then you've definitly got a vacuum leak somewhere. If you don't have a gauge, maybe just listen to it or put your thumb on it to hear/feel if it's sucking air.
That's assuming a vacuum line problem, or part of the intake has come undone. They're likely and simple culprits. But that could be barking up the wrong tree - it could be a number of things. Fuel pressure too high, no/poor ignition (coilpacks / spark plugs), faulty sensors, ECU troubles, wiring faults (if wiring has been modified), etc.