Why is my station not collecting any resources?

There are a number of reason why the industry may not be supplying any goods to your station, but the most likely reason is that the station in question have low ratings for that particular good.

Stations ratings are based on, generally speaking, how often vehicles pick up goods from the station and how much goods have accumulated there. The OpenTTD Wiki provides the complete table: http://wiki.openttd.org/Game_mechanics#Station_rating. You can see the station's ratings by clicking on the 'ratings' button in the station interface.

If your station has a lower rating compared to your competitor, your stations will receive less goods from the industry, and if it has extremely low ratings (after a vehicle crash, for instance) then the industry may stop supplying goods to that station entirely.

Also note that it is impossible to get 100% transported rate as industries do keep a certain amount of the output to themselves. (Source)

Goods won't start being delivered to a station until you send a vehicle capable of picking them up. If you're waiting for goods to appear before sending your first vehicle, it won't work.

If there are two competing stations and both of them have higher ratings than yours, new goods will only appear at those stations. Send lots of empty pickup vehicles to raise your rating.