A couple of things possible. First thought is that since the brake pedal is hard to push down, yoy have an issue with the power function of the brakes. They actually work off of the engine vacuum and are connected to the engine vacum system by a rubber hose. That hose may have come off or is badly cracked. This is an easy inexpensive issue. Could be air in the system. Start with bleeding the brakes. Usually though, when this happens, the pedal goes to the floor. Could be a problem with the anti-lock brake system electronics. Get ready to shell out big bucks for that problem.
I don't thing the ABS light would be on with a vacuum leak. The ABS system is in the electronics. Those may still be functioning properly. Many, many years ago, cars didn't have power-assisted brakes. i learned to drive on one without them. I have also driven a car that had the vacuum-assist part broken, It was exactly as you described. On those old cars, you had to push down harder, but there was no sudden grabbing. On the car with the non-functioning power-assist, it was just like you described. i bet you have a vacuum leak. They are no really uncommon. just look for a hose running up to the brake reservoir to that big round canister attached to it.