Well, brakes are always fun luckily there is only a few components to the brakes on an F-150, so we'll look at them all.
First off, check the master cylinder. When these go bad the pedal starts to drop to the floor as you depress it with your foot. Fluid will still be in the resivoir, but over time it will run out. Now it is usually a spring type valve that goes, but if you stomp on the brakes, you could do a lot more damage than normal wear and tear. If you are able to pump the brakes, and build up pressure to where the pedal feels normal, that is a good indication that the master cylinder is bad.
Second, brake lines. You have two types steel and rubber. It is very rare for a steel line to just go out and cause a leak. Most of the time it is the rubber lines that are right next to the caliper (or depending on the year, the drum). These will deteriate over time, get brittle and break, also they are subject to anythin you might run over. Usually any problem you have with a brake line will be noticed immediateltly, usually because the pedal will drop FAST to the floor, once pressed. Also the fact that you don't slow down while hitting the pedal is also a good indication. Remember a failing master cylinder will still allow you to use your brakes, just not very well.
Third, calipers and pads. Pads are easy, when they go bad, they squeal. In fact they are designed to do that just so that you know that your pads needs to be changed. Same with brake shoes. The calipers work directly with the mmaster cylinder, you press the pedal, move the spring valve in the M. cylinder, the fluid compresses and moves the piston in the caliper. Release the pedal and the reverse happens. About the only time a caliper won't work (other than a fluid loss) is if the caliper has been used in years, and they have rusted over. If a caliper stucks you are going to have a hard time going, not stopping.
My guess, based on how things work, would be that you have a bad master cylinder. Pressing the pedal really hard achieves the same effect of pumping the pedal, increases the brake fluid pressure.
As for the E. brake light, check the little switch right next to the release handle. These things are notourious for randomly going on, it is no big deal, besides you would notice if your e-brake suddenly came on. Also the e-brake is meant to keep the car from rolling away, not stopping your truck, which is why it doesn't work the same as hitting the brake pedal.