So my question is: Could a faulty check valve cause my car to have no brake pedal after I bleed the system?

Because even after I bleed my brake system I still get no pressure on the pedal. Ive bled the system three times and still nothing.. I know another possibility could be the brake booster.
Any ideas Honda-Tech?

 

could be a leak in the brake line somewhere. did you check are your lines to make sure it wasnt that?