Ordinarily, while the fish won't suffocate, if the surface of the water is calm and still, there isn't much oxygen transfer taking place.
That is the movement of oxygen from the air to the water - for this to happen at its best you need a large surface area, caused by bubbles and ripples.
I suspect what you have called the pump is probably the filter - it cleans the water and as an aside causes water movement which helps the above.
While I doubt the fish will suffocate (although I have no experience of discus and their requirements), it would be best if you could get it started again anyway, or look for alternative means to get some kind of water movememnt. We'll come onto that.
As wilder said we will need some more info, including the inhabitants (numbers rather than names if you don't know), if the tank has real plants, the lighting shedule, what and when you are feeding them and if you have anymore kit available to you.
It may be that (if you can) you'll have to visit a local fish store and they will be much more positioned to help you, with some visual clues. However, pumps/filters can be unreliable at times, and often will clog up with stuff from the tank, so you may need to get your hands wet! Of course, it could be as simple as a blown fuse?!??!?!