The ABS theory is interesting. If it's the ABS causing the issue, then
vibrations won't be the same freqency as your wheel speed. Have you ever
felt the ABS engage? (Actually, are you sure you have ABS? I'm not even
sure it was available on the 2000 Accent. If it was, then very few
Accents actually had the option.) If not, you should take the car to a
place where you can experiment safely (no danger of running into
with braking on a slippery surface. Get your car going pretty well and
slam on the brakes. When the ABS activates, you should feel the pedal
vibrate. If this is exactly the same as what you feel when braking, then
the ABS activation is likely causing the vibration you're experiencing.
The next step would be to determine whether the situation is normal.
entirely possible the ABS is activating to do its job. In such a case
there would be no need for repair. What you should be interested in is
whether any of the wheels are on a slippery surface when the vibration
occurs. Also, if it's the ABS activating normally, there's no need to
remove your foot from the brake pedal. You should continue applying
pressure to achieve the stop you desire.
More common, however, is that the front rotors are not true. To repair,
you'd need to resurface or replace the front rotors.
I'm not sure what the cause of your ticking in the dash might be, but if
the vibration when braking is enough to shake the entire car, then that
would explain the change in the ticking.