Overflow Pipe Popped off Drywell
Without knowing the construction it's tough to give you an exact answer. However, I would first try to determine what is emptying into it. Rain gutters, ground water, grey water, etc.? It's purpose may be to keep water away from your foundation. Are you having moisture problems in the house? Second, have you seen it overflow? In other words, is water coming up or is it simply not taking in the groundwater around that drain in your picture. You call it an overflow pipe. It may be that, or it could be there to drain ground water. In that case you might want to reset it below ground level allowing ground water to drain into it. In other words - a french drain.
If the drywell is, in fact, overflowing and causing problems the only way to resolve it is to excavate to see what's going on.
In that case, a septic company may be able to help you.