Broadstone was one of those strange junction stations (like Barnham, Melton Constable, Horsted Keynes etc) which brought very busy railway activity to a small place. These always had a rather odd atmosphere. At one time trains to Salisbury, Brockenhurst and the S&D ran northwards and eastwards from this location, in fact this was the case until 1964 but with closure of all these routes to passengers by 1966 things changed very quickly. The station lingered on in slowly decaying shape until 1977 when the last freight trains to Wimborne ran.
The station site today is encroached on by a sports centre, though I understand that it's easy enough to divert around it. I suspect Broadstone will once again become an important station in the future as there's been much housing and commercial development in the area, all potential future customers! The line to Ringwood from Brockenhurst is high on the list of rail revival plans, it doesn't take a lot of imagination to extend that back through Wimborne and down to Broadstone, with the line southwards to Poole obviously being restored as part of the S&D revival. Who knows, even the Salisbury line may make a comeback bearing in mind that it serves several currently thriving but road-dependent towns. In fact a 21st century Broadstone station will probably be far busier than it ever was in the 20th!