Try a few other things, only continue current exercises if by using variations suggested here the exercises are felt in the chest. On presses and in fact all chest & lat exercises, you want minimum forearm motion and maximum upper arm movement.
Keep this in mind while pressing, try doing them without hitting the top part of ROM, which is more for tris. If you do this right the upper arms will follow a ROM something like flys, and the elbows are a bigger part of the motion than the hands are. Just as with lats, you want the elbows/upper arms involved, with as little forearm motion as possible.
-If you're serious, don't train "on & off", be consistent. Hit the chest twice weekly, doing it first in the workout.
-Intensity; should be going to positive failure virtually every set, into negative failure using some of the techniques below on one set per exercises.
Take a break from BB bench if it's not working, do DB presses instead, IF you feel them in the muscles. Sometimes use a standard grip, sometimes use a hammer/neutral palms facing in grip. Also try varying the grip width from shoulders to wider than that. If none of this is felt in the chest, do other things than presses; some people get nothing out of presses and never do them.
Also try:
-Cable flys
-Cable crossovers
-Pec Deck
All of the above if done properly isolate the chest more by focusing on upper arm motion, not forearms. Forearm motion has to do with triceps, not chest.
-Pushups but using resistance
-Smith machine presses
-Chest superset using any two consecutive chest exercises without rest.
-Chest triset using any three consecutive chest exercises without rest.
-Rest-pause reps after failure
-Partials; try 2/3 range on lower and upper ROM
-Negatives
-Get rid of any/all current chest exercises that don't work, including dips and presses. Keep only what is felt in the muscle. Make sure the dips are done leaning forward with the elbows doing the work not the arms-use a fly motion that exaggerates movement of the upper arms not the forearms.
-Try different rep ranges; 8-12 is best IMO. Rest no longer than a minute between sets.