DA42 Flight Instructor reported brake failure during taxi; attempted a take off; then encountered brake failure again after an aborted takeoff. Upon exiting the aircraft; a hydraulic leak was discovered.

Narrative

Upon starting the engine and doing a break test the co-Pilot felt his brakes were not full functioning. Due to the DA42 having separate pilot and co pilot brakes myself (the PIC) decided to continue the flight as my brakes were working. Upon takeoff the power was put in at a relatively slow rate (4-5 seconds). Upon reaching 1/2 down the runway we became airborne did not get our expected performance. We set it back down and used normal braking/aerodynamic breaking rolling to the end (approx 3500+ feet remaining). Upon exiting the runway we decided we would try again with a short field T/O. We put approach flaps in (for short field) and began taxiing back. Approximately 1/3 of the way back to runway XX I lost my left brake entirely. Due to not wanting to lose control of the aircraft on the taxiway we shut down. Upon shutting down the co pilot and I exited the aircraft to inspect the left brake. We noticed smoke coming from the pad and grabbed the extinguisher. We did not use it as no flame was scene. The smoke continued for around 15-20 minutes; followed by what is ASSUMED to be hydraulic fluid fast leaking. We then discovered a NEW leak coming from the pedals of the co pilot's seat.