Brakes

It is more than likely an abs problem or a brake hose try a power bleeder but if It still will not bleed then a mechanic will need to hook his scanner up and open valves with scanner then bleed it. If it still bleeds that way then it may be a bad ABS unit which can be rebuilt.

Without touching the pedal

Have a Bobby Pin/ tiny drill bit/ anything similar ready, along with some spray brake cleaner (*Safety Glasses*)

Quickly/ Fully unscrew the bleeder and crunch out any mud/ etc. From the hole in the end and the one going in sideways at the other end. Spray it clean with the brake cleaner.

Quickly reinstall the bleeder.

Bleed.

Was this the issue?

The Medic

Then check for it being blocked you can take the bleeder screw out as long as you don't touch brake pedal and see if it is blocked at bottom. Then if all that is clear and still doesn't bleed i'd say it's the hose is bad not allowing fluid to pass.