My pressure barrel stopped pouring even though 3/4 full

There are two main types of pressure barrels, which are broadly described as top tap or bottom tap, depending where the tap is on the barrel.

If the tap is at the top of the barrel then pressure is required inside the keg to push the beer up a tube and out of the tap.

In the case of bottom taps, there is no need for pressure to dispense beer, but if there is no pressure at all then a vacuum will be created in the top of the barrel when you dispense beer and eventually it will reach a point where no beer will be dispensed until you allow some gas in to the barrel to fill that vacuum.

In both cases, pressure inside the barrel will aid dispense rather than prevent it, so what you heard was much more likely to be air getting into your barrel to replace that vacuum rather than letting gas out.

In order to keep pressure inside the kegs, it is important to ensure the beer is primed with some form of priming sugar so that secondary fermentation inside the barrel can carbonate the beer and pressurise the barrel, even then, you may find you need to top up the gas level on occasion as the beer level drops and to do this you can get barrel lids which allow you to add extra CO2 directly to the barrel either from sparklets like the old soda syphon, or from gas cylinders.